What are the positions of the different schools on a primordial mind? Different Buddhist traditions have some mention of an original, primordial mind of some sort. If there is one, what are its attributes.
Bhavanga, Pabhassara-cita and Nibbana (Theravadin perspective from Ajahn Mun's Thai forest tradition)

To get from bhavanga, pabhassaara to nibbana and understand how kamma effects are stored in the present and transmigrated to the future we have to explore some terms.

What happens in-between times when we are not thinking, when we are in a dreamless sleep? Is there still the arising and falling of consciousness (citta)?

In this tradition there is the bhavanga-citta which arise after the rebirth-linking consciousness (patisandhi-citta) that form the “life-continuum” in the next existence.


  The 'Visuddhimagga' (XIV, 114) states with regard to the bhavanga-citta: 
  When the patisandhi-citta has ceased, then, following on whatever kind of rebirth-consciousness it may be, the same kinds, being the result of the same kamma whatever it may be, occur as bhavanga-cittas with that same object; and again those same kinds. And as long as there is no other kind of arising of consciousness to interrupt the continuity they also go on occurring endlessly in periods of dreamless sleep, etc., like the current of a river. 


A bhavanga citta is a vipaka citta (kamma-result), but called bhavanga (literally meaning “factor of life”) because it performs the function of the “life continuum”.

Now we come to the question how is it stored?

Dynamically maintained throughout one life to another is just a postulation with no-doctrinal evidence: 


  “.., kamma and vipaka don't get stored into some kind of immutable and centralized "repository", instead they're continuously and dynamically re-inforced or weakened from life to life with the patisandhi citta acting as the "link".”


Now onn how kamma is stored from doctrinal text.


  “Questions about the persistence of latent dispositions and accumulation of karmic potential thus remain: once the cognitive processes are activated, are they transmitted through the six modes of cognitive awareness? If so, why do they not influence these forms of mind? If not, how do they persist from one moment of bhavaṅga-citta to the next without some contiguous conditioning medium? The bhavaṅga-citta does not directly address these persisting questions, adumbrated in the Kathavātthu so many centuries before. Nor, to my knowledge, do subsequent Theravādin Abhidhamma traditions discuss these questions in dhammic terms.”
  - Waldron, William S. Buddhist unconscious: the ālaya-vijñāna in the context of Indian Buddhist thought. London: RoutledgeCurzon, 2003. p.83.
  
  Rupert Gethin in  'Bhavanga and Rebirth According to the Abhidhamma.' in The Buddhist Forum. Vol III. T. Skorupski and U. Pagel (eds.), London: School of Oriental and African Studies, University of London, pp. 11–35.
  
  “..it does not seem possible on the basis of what is said explicitly in the texts to justify the claim that the bhavanga carries with it all character traits, memories, habitual tendencies, etc." .


From the above it appears that the Theravada Commentators have resisted the temptation to create mechanism for the "transmission" of kamma, in contrast to other traditions.

Briefly, in the tradition of the Yogacara Buddhist they have a concept of store –consciousness  (alaya-vijnana).

We shall now leave the subject of bhavanga, and how kamma is stored in the consciousness and turn elsewhere for help.

Unable to find any doctrinal support, we shall now turn to the people most qualified to speak on the subject, the meditators, who many believed to have experience the ultimate and have spoken on it and I refer to Ajahn Mun of the Thai forest tradition and he spoke of the luminous mind(pabhassara-citta)

I quote from the above link:


  “The mind is something more radiant than anything else can be, but because counterfeits – passing defilements – come and obscure it, it loses its radiance, like the sun when obscured by clouds. Don’t go thinking that the sun goes after the clouds. Instead, the clouds come drifting along and obscure the sun. So meditators, when they know in this manner, should do away with these counterfeits by analyzing them shrewdly... When they develop the mind to the stage of the primal mind, this will mean that all counterfeits are destroyed, or rather, counterfeit things won’t be able to reach into the primal mind, because the bridge making the connection will have been destroyed. Even though the mind may then still have to come into contact with the preoccupations of the world, its contact will be like that of a bead of water rolling over a lotus leaf.” ..from Ven. Ajahn Mun, ‘A Heart Released,’ p 23. Found in Ajahn Pasanno and Ajahn Amaro, The Island: An Anthology of the Buddha’s Teachings on Nibbāna, pages 212-213.


In the same link above Pabharassa-citta is identified as bhavanga.


  “The Theravadin Angutta Nikaya Atthakatha identifies the luminous mind as the bhavanga, the "ground of becoming" or "latent dynamic continuum", which is the most fundamental level of mental functioning in the Theravada Abhidhammic scheme.[11] Thanissaro Bhikkhu holds that the commentaries' identification of the luminous mind with the bhavanga is problematic, but Peter Harvey finds it to be a plausible interpretation.
  In Thanissaro Bhikkhu’s translation of the Pabhassara Sutta he gives his reason in Note 1.


(I’ll refer to Note 1 to it later).
I do not have access to Peter Harvey’s views. But in the Brahma-nimantanika Sutta(MN49) translated by Thanissaro Bhikkhu, there is a description of “'Consciousness without surface, endless, radiant all around” and in his Note no. 9 in MN49 he argues that:


  Consciousness without surface (viññanam anidassanam).. for the arahant, nibbana is not an object of consciousness. Instead it is directly known without mediation. Because consciousness without feature is directly known without mediation, there seems good reason to equate the two.


That this consciousness is Nibbana!

But yet in his Note 1(which I promise to come back) in Pabhassara Sutta  he says:


  Another interpretation equates the luminosity of the mind with the "consciousness without feature," described as "luminous" in MN49, but this interpretation also has problems. According to MN 49, that consciousness partakes of nothing in the describable world, not even the "Allness of the All," so how could it possibly be defiled? And, because it is not realized until the goal of the practice is reached, why would the perception of its luminosity be a prerequisite for developing the mind? And again, if "mind" here means consciousness without feature, how could the sutta talk of its development?


Here is Ajahn Sujato's Pabhassara reading that the mind is somehow radiant!


  The beginning of the Sutta has the Buddha (presumably, although it doesn’t actually say so), saying, “This mind is radiant…” The particle “idam”, “this”, functions to limit and specific: This mind, not “the mind” (as in Thanissaro’s translation). As well as the gold/samadhi passages, we might compare to the Upakkilesa Sutta, where the Buddha speaks of how he meditated, then light arose, but because of “defilements” (upakkilesa, the same word as our sutta), the light vanished. The word for light is different (obhasa), but is from the same root with the same basic meaning. 
  
  This is the normal way the Buddha talked about the mind. It is not that it is “naturally” radiant or defiled: it is naturally conditioned. When the conditions for darkness are there, it is dark, when the conditions for light are there, it is light. Our passage, which is unique, without parallels in any early Suttas, syntactically awkward, clearly the subject of editing, can be read as suggesting a different take on things, that the mind is somehow “radiant” even when covered by defilements. Or it can be read in line with the other, more clear suttas.
  
  In either case, there is no suggestion here that the “radiant mind” be connected with Nibbana. Quite the opposite: the whole point of the sutta is that it can be defiled, so it cannot be Nibbana.


Ajahn Sujato stop short of connecting the "radiant mind" with Nibbana because ..it can be defiled.

The answer is provided by Ajahn Mun’s description:


  “The mind is something more radiant than anything else can be, but because counterfeits – passing defilements – come and obscure it, it loses its radiance, like the sun when obscured by clouds”…. “When they develop the mind to the stage of the primal mind,..”


So in the Pabhassara sutta  when it is said:


  “Luminous, monks, is the mind.[1] And it is defiled by incoming defilements." {I,v,9}
  
  "Luminous, monks, is the mind. And it is freed from incoming defilements." {I,v,10}
  
  "Luminous, monks, is the mind. And it is defiled by incoming defilements. The uninstructed run-of-the-mill person doesn't discern that as it actually is present, which is why I tell you that — for the uninstructed run-of-the-mill person — there is no development of the mind." {I,vi,1}
  
  "Luminous, monks, is the mind. And it is freed from incoming defilements. The well-instructed disciple of the noble ones discerns that as it actually is present, which is why I tell you that — for the well-instructed disciple of the noble ones — there is development of the mind." {I,vi,2}


Both Ajahn Mun and the Buddha are saying the same thing but Ajahn Mun had clarified that the luminous mind has lost it radiance when it is obscured by defilements and that we have to get rid of the defilements to reach the state of the primal mind (why would we want to go back to the primal mind, only if it is inherently luminous).

The Buddha stated very clearly that whether the mind is defiled or not it is still an inherently luminous mind. (inherently - my addition in light of Ajahn Mun's clarification)

Is an inherently luminous mind therefore the same as "consciousness without feature" i.e. Nibbana?

What Ajahn Mun's has said is that the primeval mind is defiled in the way of being obscured by defilements and not as altered ". What is intrinsically bright cannot be defiled by alteration but can be obscured, ...like the clouds covering the sun.

The inherent luminous mind obscured by defilements is therefore bhavanga.

1) So is the true characteristics of Bhavanga, Pabhassara and Nibbana, the same, "consciousness without feature", except that Bhavanga has defilements obscuring its true nature?

2) Or is Bhavanga and Pabhassara the same, both luminous primodial mind, and different from Nibbana?

3) Or is Pabhassara, a luminous primodial mind with Avijja, not the same as Nibbana, pure awakened mind with vijja and Bhavanga just "emanations" of Pabhassara?

The Thai forest tradition of Ajahn Mun seems to adopts the third view.