@Setanta,
I'm with you. I'm really, really tired of internet pissing contests and I've no interest in trying to one-up you. As far as I can tell, we agree a helluva lot more than we disagree. I would like to pick your brain a bit, as you have some knowledge that I don't, and if you're interested, I'll share what I've read, seen and heard.
As for a non-self rebirth, Adrian Kuzminski has done the best work on that that I've run across so far, but Robert Gombrich has also contributed a great deal. Much of what follows is from them.
But before one can understand non-self rebirth, I think it's necessary to know the details of non-self. There is a conventional definition of "self" and a strict definition. The conventional concept is that a new, singular, discrete being comes into existence at birth (or thereabouts), maintains its unique identity throughout its lifetime, and the same person dies that was born. Conventionally, that's very a useful and perhaps even necessary way to treat experience.
However, strictly speaking, nothing new is created when a baby comes out of a womb (or when its gestating). This is the reductionist approach. Matter and energy are conserved. The baby is the product of the mother's nutrition. Science tells us that all the matter in the human body is replaced every 7 years. Cells (even deep bone cells) wear out and get replaced. So, physically speaking, how is an adult the same person that came out of the womb? S/he isn't.
As for the persistent
sense of being a singular self, that's just an illusion created by the sense of continuity that comes from storing memories, feeling sensations locally in a single brain, being called the same name year after year, etc.
Paticca samuppada is the observation that present states are conditioned (not strictly causal) by previous conditions. Nothing groundbreaking in itself, until you add to it the concept of
anatta. The present (persistent) sense of being a self is the result of the conditions leading up to having this particular kind of brain. This particular kind of brain produces a sense of agency, which is
the illusion of the self.
It can be turned off by anesthesia, whacks to the head, etc. But do we say that the person ceases to exist when the sense of self is turned off? No, because our sense of self is projected onto others.
The Buddha's take on this is predictably archaic. Instead of the sense of agency, he analyzed the human experience into 5 khandas, which you are probably familiar with. The physical body and the various kinds of mental experience. Ear-consciousness, eye-consciousness, etc, the contents of which are changing constantly from moment to moment (
anicca). Nothing is permanent. Then he says that he sees nothing more to a human than those 5 khandas, and that neither the body nor any consciousness is reborn.
The human, then, is just a bundle of phenomena that are conditioned by previous phenomena. Not a self in the conventional sense. The human isn't a singular, discrete entity that endures from birth to death. But it's not nothing, either. Something is going on, and it's being experienced.
So, finally, we get to what is reborn. It can only be impersonal phenomena, maintaining the conditional continuity of all phenomena. The behavior of one (apparent) being affects its environment. The repercussions bear fruit of some sort in the future. The words you speak today can continue to affect some other consciousness long after you're dead. (Gautama was only interested in human experience, not cosmology.) That effect, if it's strong enough, conditions that person's behavior and is "reborn" in that behavior, with either good, bad or neutral results.
Once you get past the idea of being a discrete entity, it makes logical sense to say that the components of your apparent self are just steps in a long chain of conditioned phenomena, and there is no 'you' anywhere in it. Your grandparents' boinking one night decades ago contains something of "you" in this conditioned phenomenalism, just as what you do today will condition future phenomena that can just as rightly be called "you."
And nowhere in any of that is superstition, as far as I can tell. Now, do I declare that all of this is what the Buddha meant? How would I know for sure? I take the Pali Canon with a grain of salt, just like everything else. However, logically speaking, the combination of
anatta, paticca samuppada and
anicca add up to this very mundane conceptualization. I don't claim to know whether it's true or not; I'm just presenting my current understanding, but it does appear very logically, internally consistent and does not contravene what I know of modern science, and at least some of which is lately being confirmed by neuroscience.
Jeez, I can be long-winded. Sorry about that, but it's a complex topic. I'd be interested in knowing if you see any weak links in that. I'd appreciate the feedback.