The string theory description will possibly be that the black hole (the big ball of strings and branes created by gravitational collapse) loses most of its energy over time by shedding Hawking radiation, and also shrinks until it's smaller than the curled-up dimensions - at which point it will be as small as an ordinary string, and all the space dimensions around it will look "big" to it - and then it just blows up into a few ordinary strings. This is discussed briefly in an appendix of
http://arxiv.org/abs/hep-th/0507219 - but it's still just something of an idea, apparently the real math still hasn't been done.
In string theory, people now generally don't believe that black holes produce baby universes, because of the "AdS/CFT correspondence", which says that string theory in "AdS space" has an alternative, totally equivalent description - the "CFT" - which is self-contained, therefore the strings can't ever be creating new degrees of freedom that aren't in the CFT, like a new universe. And then the presumption is that this must apply to string theory in any space, even if we don't know the counterpart of the CFT description for our sort of space.
But even in AdS space, the study of how black hole processes correspond in detail to the CFT description is still quite schematic. It does occur to me that ultra-high-energy virtual processes in the CFT might correspond to the branching off of a closed universe on the AdS side. This is a loophole which has to do with how modern quantum theories work.
To get the probability of starting with some observed physical situation A, and later obtaining another observed physical situation B, you do Feynman's sum over all possible histories starting with A and ending with B - the path integral - and it's a bit like ordinary probability (where you add the probabilities of the individual possibilities, in order to get the total probability), except that you use complex numbers and so different histories can cancel. So this is the mystery and scandal lying beneath the empirical success of quantum mechanics, that we have this procedure for generating empirically relevant predictions - probability of B given A - but we don't know what the hell it means that we have "cancelling possibilities" in between. I actually don't think the idea of cancelling possibilities makes sense in reality, so there must be some other picture of reality that provides an alternative justification for the success of these Feynman calculations.
But even putting that issue side, there are also mathematical technicalities to Feynman's procedure which mean that when it is actually done, it's not as straightforward as it sounds. Suppose you're doing a sum over histories for a vibrating string. You're supposed to include "all" possibilities. Does that include histories where the string is fractally bent, down to infinitesimal scales, and not just where the string is smoothly curving? It ought to, but there are severe mathematical difficulties in defining the path integral over "all infinitesimally jagged string configurations". And the analogous problem arises for fields - in this case the problem comes from peaks and troughs in the field intensity, that have that same infinitesimal jagged fractal quality.
So in practice, these sums are only done over limited classes of configurations, and then there will be some recipe for approximating or ignoring everything else. If this recipe works, meaning that you can still get meaningful answers from a procedure consisting of "sum over histories but throw away the infinitely jagged ones", the theory is called renormalizable (since you "renormalize" various quantities in the cutoff theory, in order to extrapolate what the full theory would have said) and it's considered a mathematical success.
I've gone on quite a tangent, but the point is that a full sum over histories for branching and joining strings should include outcomes that look like finite baby universes - it's important that they are finite, so there aren't extra degrees of freedom at the final stage, the B that follows the A. But it seems like you ought to be able to have arbitrarily big baby universes in the path integral, and that they ought to correspond to ultra-high-energy fluctuations in the alternative, CFT description. And it may be that this aspect isn't even addressed by the nature of the approximations that are used in concrete investigations of the AdS/CFT correspondence.
That digression aside, it's also true that the ultimate outcome of black hole collapse and evaporation is still just unknown, even as a matter of theory, and it's likely that even your specific notion of some dimensions shrinking while others expand could be the basis of a concrete model, because it resembles a known type of oscillation in general relativity, I think called a Taub oscillation, where one direction of space shrinks while another expands.
The situation in physics about these questions might be remotely analogous to consciousness in neuroscience - there's a lot of data (here the data would be concrete calculations made within specific frameworks) but it's also still very unclear how it will all fit together. The picture that I started with (black hole shrinks to a single heavy string, shedding energy as it goes, and then the final remnant blows up into a handful of ordinary strings) seems appealing and plausible to me, but that's just a tentative judgement call and I wouldn't absolutely rule out the baby universes yet.
