The PICA is a truly fascinating vessel.  Its evolution in terms of cerebellar supply and secondary balance with superior cerebellar artery and AICA, give rise to unprecedented variability.  Because of its developmental relationship to the posterior spinal (lateral spinal) system, its behavior is unlike that of SCA and AICA.  The territories of the PICA are morphologically and functionally diverse, with a consequent range of clinical deficit produced through its dysfunction. 
Conceptual homology of vertebrobasilar and spinal arterial anatomy
A thorough discussion of the PICA can not be effected without a preliminary excursion into the organization of the vertebrobasialr system as whole.  I think it is time well spent.
The basilar artery is formed by fusion of the longitudinal neural system, which in its most primitive form consists of loosely connected channels running along the undersurface of the brainstem. Lasjaunias and his collegues view arterial system of the brainstem and cerebellum as a natural extension of the segmental arrangement found in the spinal cord.  The conceptual brilliance of this view allows one to understand all the myriad variations to which the basilar artery and its daughter vessels are subjected. In other words, if you consider the basilar artery to be a continuation of the anterior spinal artery, and its named branches and perforators as homologs of the coronary and sulco-comissural arteries (see Spinal Vascular Anatomy section), then the overall arrangement and its possible variations make perfect sense.
The following diagrams serve to illustrate this concept.  On a personal note, I generally find anatomical diagrams to be at least somewhat wanting; when applied to the living body, they too often suffer from both rigidity and inconsistency, and almost universally fall short of the predictive potential for which their creation was originally intended.  In this case, however, I believe that the genius of Lasjaunias (and supporting giants), may prove an exception.  It is not, by any stretch, The Periodic Table, but some time investment into a bit of theoretical discussion is likely to produce major dividends.
Below is a diagram of cervical spinal vasculature (left), and brainstem vasculature (right), without the cerebellum.
The image on the LEFT represents cervical spinal cord arterial supply, which consists of the anterior spinal artery and a paired, loose network of posterolateral vessels known as the posterior spinal arteries, and which are conceptually represented here as contiguous vessels (which is at least mostly true in the cervical spine).  The anterior and posterior spinal systems are connected by anastomoses running along the circumference of the cord, although known as “coronary” arteries, are conceptually quite clear.  A number of perforating arteries into the substance of the cord exist; when arising from the anterior spinal artery and penetrating through the ventral cord sulcus, they are named “sulco-comissural” arteries.  The entire spinal cord system is supplied via segmental radiculomedullary arteries, which connect the vertebral artery to the anterior spinal artery.  In practice, as you know, the radiculomedullary and radiculopial arteries are fewer, and may arise from longitudinal vessels other than the vert.  Radiculopial arteries are those which supply the posterior spinal system.  Radiculomedullopial arteries are those which happen to supply both anterior and posterior spinal systems simultaneously, sometimes via a coronary artery, and at other times via separate connections to the posterior spinal system. For a more complete discussion of spinal vasculature, see Spinal Vascular Anatomy section, particularly Spinal Arterial Anatomy.
Now, lets add the brainstem to the spinal cord, and use existing arterial vascular networks to furnish its supply.  Think of the brainstem as just a somewhat larger diameter biomass than the spinal cord, and things start to make sense. The unapaired basilar artery is a homolog of the equally unpaired anterior spinal artery.  The intracranial vertebral arteries, although obliquely oriented, are essentially homologs of the radiculo-medullary arteries, inasmuch as they serve as trasverse connections between the extraspinal vertebral system and the anterior spinal axis.  The transverse pontine arteries are homologs of the coronary arteries.  The basilar perforators are homologs of the sulco-comissural arteries.  The posterior spinal arteries, in the superior cervical spine, are sometimes termed “Lateral spinal arteries“.  This creates much unnecessary confusion, but the posterior spinal system and lateral spinal system are one and the same longitudinal arrangement. 
Now, add a cerebellum to the back of the brainstem, — again, simply more biomass — and use existing arteries to supply it.  As the cerebellum develops, some of the transverse pontine perforators are recruited to capture the cerebellar hemispheric territory.  Superiorly, this happens repatively consistently, and produces what is known as the Superior Cerebellar Artery.  At the mid to lower basilar segment, a homologous enlarging channel is the AICA.  At the bottom, the Posterior Inferior Cerebellar Artery (PICA) is the latest addition to cerebellar supply,  Unlike AICA and SCA, it seems to arise from the lateral spinal system (yet nervertheless also a coronary artery homolog).  The vermian arteries (of which only inferior is shown here) may be regarded as homologs of the sulco-comissural vessels. 
There are many advantages to viewing the vertebrobasilar system in this way.  All kinds of variants become quite predictable.  For example, duplicated and triplicated SCAs and AICAs are simply persistence of adjacent transverse pontine (or midbrain) arteries in supply of the cerebellar hemisphere.  AICAs arising higher or lower along the basilar are either results of dominance of higher or lower transverse arteries, or consequent to a relatively “short” basilar artery fusion.  C1 origin of PICA reflects dominance of the C1 radiculopial artery, which via the C1 segment of the lateral medullary artery, gives rise to the PICA.  The AICA-PICA balance in extent of cerebellar territory capture is a consequence of either anterior spinal (AICA) or lateral spinal (PICA) dominance.  All of these cases are given angiographic illustrations below.  For a clinical case, see Lateral Spinal Artery Aneurysm.


Basilar artery perforators
Classical dispostion depicts AICA and SCA arising from the basilar artery, in addition to multiple short basilar perforators whose supply is limited to the brainstem.  Understanding the embryology of vertebrobasilar circulation helps explain many variations seen in this pattern.  As explained above, one can think of the basilar as a longitudinal channel, with multiple trasverse channels.  As the cerebellum develops, some of these transverse channels enlarge to capture the cortical territory of the cerebellum — thus becoming AICAs and SCAs.  Others stay relatively small and are thus “limited” to brainstem supply.  This simple concept explains ALL variations seen in the area.  For example, duplicated SCAs and AICAs are just two adjacent perforators, which persisted in co-dominance of cerebellar supply.  Dominant AICAs and PICAs and SCAs are simply variations in extent of cerebellar surface capture by one vessel, with corresponding dominance or hypoplasia of the others.  “Larger” vs. smaller basilar perforators are but transverse channels which may capture some small segment of anterior cerebellar surface that is not taken by adjacent AICAs or SCAs.
Also important to recognize is the fact that brainstem perforators usually “arise” from SCA and AICA — or, rather, that AICA and SCA in fact “arise” from such perforators.  Important, though very small and thus typically angiographically invisible, collaterals exist between these perforators.  It is probable that extent of such collateral supply underlies the tremendous clinical recovery occasionally observed following ischemic brainstem infarcts.
Almost always, one or more “large” perforator is present between the AICA and the SCA — so consistently visualized, in fact, that it might almost deserve a unique name (we thought to name it “ziggy” — or rather “Arteria ziggus basilarius” — until we found out that it already has a name — “Transverse Pontine Artery”).  Occlusion of these transverse pontine arteries typically corresponds to ventral pontine infarction, and may lead to the ischemic cause of dreaded “locked in” syndrome.
Diagram of the above concept.  Image on left, with brainstem alone, shows schematic of vertebrobasilar system with numerous “transverse” perforators supplying the brainstem (transverse pontine arteries).  Image on right, with cerebellum in place, depicts SCA, AICA, and to some extent PICA as perforators which enlarged to capture cerebellar hemispheric territory.  This viewpoint allows for ready conceptualization of multiple SCA, AICA, and PICA variations observed within the vertebrobasilar system.
The unique nature of the Posterior Inferior Cerebellar Artery
Now we are in a better position to do justice to the PICA.  For the above discussion emerges a view which conceptualizes the PICA as a branch of the lateral spinal artery — as distinct from AICA and SCA, which are branches of the Anterior Spinal Artery.  All of these vessels (AICA, PICA, SCA) are, essentially, coronary vessel homologs of the spinal cord (see the very first diagram — essentially transverse vessels running on the surface of the cord, or brainstem).  All three have enlarged to support the cerebellum, and in that territory are in balance with each other.  Variations in origin, number, and position of the SCA and AICA are discussed in their respective sections — and, because of their relationship to the ASA, their variability is chiefly of position and number.  The spectrum of PICA variants, however, is quite different, and it is here that conceptualization of PICA as a lateral spinal artery shows its brilliance.  The idea is that the medullary segment of the PICA is, in fact, an enlarged lateral spinal artery, whereas the vermian and cerebellar branches of the PICA are “coronary” type vessels originating from the “lateral spinal — PICA”, in the same way that SCA and AICA are coronary vessels of the ASA.  Here are some “proofs” of the concept:
First, unlike SCA and AICA, the first segment of the PICA, in its classical disposition, is responsible for support of the lateral medullary territory — similar, of course, to the “lateral spinal” system of the cord.  The clinical correlate of this is, of course, the lateral medullary syndrome of Wallenberg (and its several variations), which results from vertebral artery occlusion at the PICA origin segment (an appropriately sized embolus gets stuck in the smaller caliber vert past the PICA origin; a yet smaller embolus may lodge somewhere more distal in the basilar or PCA).
Second, the frequent variations in origin of the PICA vis-a-vis the vertebral artery are easily explained via the lateral spinal homology.  For example, C1 or C2 origin of the PICA represent lateral spinal artery course from C1 or C2 segments rostrally, to “end” in the usual PICA. The variation is thus explained with existing vessels with no need to invent new ones.
Third, frequent observation of lateral spinal artery origin from the PICA is fact represents the inferior aspect of the lateral spinal system which includes the larger-sized PICA component.
For an excellent review on the subject, read an article by F. Siclari, I.M. Burger, J.H.D. Fasel, and  P. Gailloud: Developmental Anatomy of the Distal Vertebral Artery in Relationship to Variants of the Posterior and Lateral Spinal Arterial Systems.  AJNR Am J Neuroradiol.  2007; 28(6):1185-90 (ISSN: 0195-6108).  Link to full text/PDF: http://www.ajnr.org/content/28/6/1185.full
Below are some illustrations of the above concept.
Extradural (C1) origin of PICA — angiographic views of C1 origin PICA (red arrow), and diagrammatic representation of this disposition, highliging the lateral spinal origin of PICA.
C1 origin PICA with medullary segment “perforator” at classical PICA origin — illustrating the concept of PICA relationship to the lateral medullary artery, and the role of segmental organization.  In this patient, dominant PICA originates at hte C1 segment (red).  As is often the case in such situations, the medullary territory normally supplied by the PICA is now under control of a small medullary “perforator” (yellow) which takes off at the location where classical “PICA” would come from.  The clinical implication of this arrangement is that occlusion of C1 origin PICA may not produce the classical lateral medullary syndrome; — the clinical deficit in such cases is congruent with the vermian and cerebellar hemispheric PICA territory and extent of collateral support.  A related situation is a well-known AICA-PICA variant, where AICA captures a variable amount of PICA territory, including hemispheric and vermian, but almost never the lateral medullary segment.
Also see a case of Lateral Spinal Artery Aneurysm.
Here is another beautiful example of C1 origin PICA (green), “giving rise” to the lateral spinal artery (yellow), which shows the embryologic relationship of the PICA to the lateral spinal.  The “true” location of the PICA is shown by the large lateral medullary perforator branch (pink) arising from the intracranial vertebral artery.  The upper cervical portion of the Anterior Spinal Artery (red) also arises from the same level. 
This is to show that the PICA indeed arises below the foramen magnum, in this straight AP view.
Below are two diagrams of the classical disposition of PICA  on left, and the C1 origin on right.
Duplicated PICA
As in everything (like PCOM/P1) there is a balance.  The above cases show dominant C1 origin PICA with a small intradural vertebral artery lateral medullary perforator.   The case below, very rare, is a more obvious “duplicated” PICA where the C1 origin PICA supplies lateral inferior cerebellar hemisphere as well as a large posterior meningeal artery, while the intradural PICA component supplies the medullary and vermian segments.
Cross eye stereos
Anaglyph Stereos
C2 PICA Origin — look for them before you buzz them
This one is less commonly seen, but is no different than C1 in principle — just a lower origin lateral spinal homolog.  Again, it is key to understand that 1) lateral medullary supply will not come from the PICA, but will arise directly from the vert, and 2) the cervical PICA may contribute to supply of the lateral cord as the lateral spinal artery, and so must not be sacrificed without extreme caution. This image shows the C2 radicular branch (red) supplying the lateral spinal artery (white), with the tonsillar PICA segment in purple.  Although the whole thing is just called “PICA” it is critical to understand that it is a very special kind of PICA, where the proximal part is made of the radicular C2 branch and the lateral spinal artery.
Lateral stereo view shows the lateral medullary perforator (yellow) in location of the classical PICA origin.  The arrows point to the same structures.
Stereo native image, demonstrating PICA arising below C1, at C2 segmental level

Lateral Spinal Artery / C1 radicular artery / PICA anastomosis

Lateral spinal artery is a pathway by which PICA can be reconstituted in cases of more proximal vertebral occlusion — again recognizing that PICA is a lateral spinal artery homolog — in effect an enlarged lateral spinal artery capturing territory of the cerebellum in addition to the lateral medulla.  In this patient, the right vertebral artery is occluded just below the foramen magnum due to dissection.  The C1 radiculopial artery (purple) connection to the lateral spinal artery (red) allows for reconstitution of the vermian branch of the PICA (black).  The lateral spinal artery inferior to the C1 radiculopial artery is marked with a pink arrow.  Notice also presence of the anterior spinal artery (yellow) perfectly contrasting its anterior and medial position to that of the spinal artery.  The C1 radicular branch (purple) is in effect the radiculopial artery is acting as a radiculopial artery, homologous to radiculopial supply of the posterior spinal arteries at the thoracic and lumbar levels (see Spinal Arterial Anatomy) The C1 muscular branch (green) opacifies the occipital artery (white) and deep cervical artery (blue).

Lateral Spinal Artery

The indispensible STEREO pair

Lateral Spinal Artery

Inferior Extension of the PICA into the Cervical Spinal Canal
Just as the PICA can have an intradural course with a cervical origin, the same embryonic route can be used for the vessel to loop down into the cervical canal (medullary loop) and then head back up into the head.  Here is one such example, in stereo, of bilateral such PICA dispositions.
PICA cervical extension
Native image, stereo:
PICA cervical extension native
PICA occlusion and the lateral medullary syndrome
The clinical syndrome of PICA occlusion (Wallenberg and its various partial forms), a.k.a. the lateral medullary syndrome, is a clinical testament to PICA association with the lateral spinal artery.  The syndrome is occasioned by occlusion of the PICA ostium (usually by thromboembolus lodging in the vert against PICA origin, or via vertebral dissection).  The very proximal medullary portion of the PICA typically sends a lateral medullary branch to the lateral medulla, corresponding to the lateral spinal artery of the cervical spine. Here is a classical lateral medullary MRI/MRA, demonstrating acute infarction and apparent distal vertebral occlusion on MRA
Angiogram of the same patient shows that the vertebral artery is, in fact, open, with a faintly seen stump of the lateral medullary artery on left and center frontal and lateral projection angiographic views.  Paired images on the right, post intra-arterial heparin, show more fully the distribution of the lateral medullary artery, with post-reperfusion hyperemia.  The patient did very well.
Occipital origin of PICA
Just as in the above diagrams the extradural origin of PICA is part of a connection between the vert and occipital artery at C1, in the same way the extradural PICA can originate from the occipital artery just as well as it can from the vert.  It is far less common, but the important point is that both dispositions are predictable based on the embryonic connections between the occipital and vertebral arteries.  In fact, both occipital and vert origins of PICA are, in a way, extremes of a continuum.  Functionally we often see reflux of contrast into the vertebrobasilar system during occipital injections, and more frequently C1 origin of the occipital artery from the vert. All of these are possible variations on the theme of transverse/longitudinal organization.
In this case, courtesy of Dr. Antonio López-Rueda from Hospital Clínic i Provincial de Barcelona (alrueda81@hotmail.com), an isolated PICA (red arrows) is opacified via injections of the left occipital artery (white arrows).
A diagram of this disposition is shown below:
Note please that the above case and diagram are exactly the same as that of the Proatlantal artery disposition, except that the PICA is isolated and therefore there is no occpital supply to the basilar.  The proatlantal artery is just an occipital artery with a persistent connection to the vertebrobasilar circulation, Type 1 at C1, and Type 2 at C2.  Below is a diagram of the C1 type.
AICA-PICA balance 
Probably the best known variation of the entire cerebral circulation (excepting, maybe, the fetal PCOM), and perfectly illustrative of the above concepts.  In the simplest form, the AICA is big, and PICA is nowhere to be found, and so an “AICA-PICA” is called.  The same is not said, however, when the reverse is true, and the AICA is “missing”, where a “PICA-AICA” would be equally appropriate.  In fact, there is a continuous distribution (probably Gaussian) in the AICA-PICA balance.  Extremes of left and right are represented by apparently “missing” AICA or PICA, whereas the contiuum is reflected in the relative sizes of the two vessels, as required by the relative size of the territories they supply.  For example, the AICA may capture more or less of the hemispheric territory of the PICA, or may take over both hemispheric and vermian areas.  But there is NEVER a situation where the is no PICA, or no AICA — ALWAYS there is a small PICA, though perhaps too small to be seen on MRA or CTA.  When does an AICA get so dominant as to capture the lateral medullary territory of the true PICA — I have never seen a lateral medullary infarct due to AICA occlusion.  In the same fasion, when does occlusion of dominant PICA produce a ventral pontine infarction, as would be expected in case of its compete capture of the AICA domain?  And, to make things more complicated, there is not infrequently a situation where one PICA takes over the hemispheric and vermian territories of its contalateral homolog, so that one sees a very large ipsilatearal PICA, and hypoplastic contralateral PICA and AICA, as an incidental variation with no clinical deficit.  All of these dispositions illustrate highly variabe arrangement in regard to cerebellar vascularization, and relative rigidity in control of the brainstem territory.
In this diagram, the right AICA is dominant and supports PICA hemispheric and vermian territories; only the lateral medullary territory stays constant to a small PICA, which is not often appreciated as such on angio, and even less so on CTA/MRA.  But there is ALWAYS some part of the PICA present, even if tiny. On the left, PICA dominance is depicted, with a relatively hypoplastic AICA. 
“Azygous” PICA supplying both cerebellar hemispheres
Right PICA (red) supplying both cerebellar hemispheres.  The left PICA is not visualized (top left image)
MRA volume rendered image of biphemispheric PICA — notice bilateral hypoplastic AICAs and one large PICA
Movie of same case — pause to scroll
An even better case of bihemispheric PICA supply — with a stroke.  See full case “Bihemispheric PICA stroke with Lateral Spinal Artery PICA reconstitution” on the Instructive Cases page

bihemispheric stroke LSA reconstitution of PICA

Frontal and lateral angiographic views show occlusion of the left PICA (white arrow) beyond the medullary segment (purple arrows).  Notice clot in the proximal medullary segment, best seen on lateral views.  The is a dominant large PICA with variant bihemispheric supply (pink and black arrows).  Notice truncated appearance where black arrows are corresponding to distal embolic occlusions.  the parenchymal blush is outlined by green arrows.   How is the PICA reconstituted — the most common way it is — via the Lateral Spinal arterial network at C1 (yellow) and proximal intracranial (red) segments (also see examples below).  Notice inferior component of the lateral spinal artery (brown arrow) just below its C1 segment (red arrow).  Brown arrow points to the more typical length of the lateral spinal artery, when seen angiographically. The anterior spinal artery is shown by blue arrow, and is of course anterior to the lateral spinal artery.  This kind of reconstitution has a propensity to form flow-related Lateral Spinal Artery Aneurysms so follow up is needed.

bihemispheric stroke lateral spinal reconstitution of PICA

Third case with anaglyph stereos

Dominant left PICA supplies left lateral hemisphere and vermis.  Small PICA on right goes to lateral hemisphere only.  Small AICAs supply the IAC area (they nearly always do).  Both SCAs supply the lateral hemisphere territory of AICAs. In the end, its  bumper sticker, and everyone here is actually happy

PICA – SCA Balance

Much less mentioned than AICA-PICA, but its real.  The balance is mainly in suppy of the vermis (AICA-PICA is usually lateral / hemisphere balance).  The superior verims is SCA, inferior is PICA classically.  Below is an example of dominant SCA supply of vermis (solid oval), with a correspondingly small PICA (dominant AICA supplies hemisphere and some inferior vermis, dashed oval)


PICA Fenestration

another curiosity, next to an unusual aneurysm arising distal to the PICA ostium.  One should at least consider the possibility of dissecting pseudoaneurysm — an incidental finding in this patient. STEREO PAIR.

Dural ring and extradural PICA
Many times one osberves a change in caliber of the vert (for the smaller) when it pierces the dural ring of the foramen Magnum — not to be confused for a stenosis or dissection, etc.  The same phenomenon is seen for other vessels entering the foramen — namely the extradural PICA (when the pica arises outside of the dura below skull base).  In this patient with a generous left vert injection refluxing into the contralateral right vert, the dural ring impression can be seen on both verts and right PICA (red arrows).  The significance of having an extradural PICAis that a PICA origin aneurysm is extradural also; other surgical considerations are also present.  Notice also a small basilar fenestration (yellow)