Disclaimer: I don’t know or pretend to know how consciousness arises; this is for entertainment purposes only. 
Please also note that this is only drawing from my experiences and thus doesn’t include the effects lucidity has on DC vs the dreamer.
A thread on another forum got me thinking about the structure of DC and how they arise. In my own experiences, there has been little difference between DC and dreamer during dreams. DC change appearances at random, but the dreamer often has no concept whatsoever of his own appearance and wouldn’t know whether or not s/he was changing or not. Both DC and dreamer randomly appear and disappear in the middle of dream scenes, as evidenced on the part of the dreamer by the fact the dream will often start in the middle of a dream’s plot and wake up before the end as well as have quite a few scene skips during an average dream. If someone played back a dream as a movie from a third person point of view, there probably wouldn’t be any real way to tell who was the dreamer.
When looked at this way, it is possible to come to the conclusion that DC and the dreamer are all beings of the same make that are essentially consciousnesses produced and maintained by the SC. The only difference between the two is that the dreamer maintains his memories upon awakening whereas the dreamer doesn’t maintain any memories from the DC. This doesn’t necessarily mean that all DC are created equal, though. There are some DC that clearly have more resources put into them than others. As would be expected, DC that just pop in and out or are only intended as a minor plot device may be run on a very basic AI (and may or may not apply to this model as opposed to one for, say, a DO).
Basic illustration:
If this model is taken for a moment as true, there are two possible explanations for the consciousnesses behind various DC. The first is that at the end of the dream, the SC reabsorbs the DC and assimilates their experiences into itself, and at the beginning of the next dream it will create new DC out of itself to restart the process. This seems likely for the majority of DC. The second explanation is that there is one or more secondary consciousness that maintains one or more DC. The DC may not maintain the same appearance in every dream (or even in any two dreams), but the personality behind the DC should be the same every time. This would potentially be the case in cases such as DG (not SG) and RDC.
(Conjecture: If this were true, it would indicate the possibility that REM periods with no recall could be dreams in which the dreamer was not a participant.)
tl;dr
Hypothesis:
- The dreamer is a division of the subconscious that is active during waking periods as the exclusive controller of the body in healthy humans.
- During dreams, the dreamer takes part as a DC.
- DC are also a division of the SC similar to the dreamer in structure and proportionally similar in intelligence.
- DC are consciously separate beings from the dreamer. (They all stem from the SC, but on the level of consciousness they are separate from the dreamer.)
- DC possess, or at least are capable of possessing, all of the same mental and emotional capacities as the dreamer.
- As a correlary to 2 and 5, the dreamer possesses the same mental and emotional capacities as DC during the dream.
One potential problem with this hypothesis is that if all DC are conscious entities originating from the same mind, why don’t we remember things from our DC’s point of view? To this, I propose one of two potential answers. The most simple of these is that DC don’t record memories during the dreams and because of this there is nothing to remember. This is supported by the fact that even the dreamer often won’t remember things that happened from dream to dream (or will be given false memories) but is contradicted by the fact that the dreamer remembers his dreams upon awakening. The second possibility is that the memories of the DC are separated from that of the dreamer in the same (or a similar) way as memories are separated between alter egos in people who have multiple personality disorder.