One of the current theories relies heavily on the theories of quantum and states that the singularity may not form at all. Instead, at 10 to the -33 centimeters, time ceases to be present and only space is relevant. This, of course, disallows the formation of a singularity, but under ideal circumstances, i.e. no external forces acting upon a perfectly spherical star at all, then the singularity might still form. These calculations are based entirely upon quantum mechanics, since they are more accurate at such minute distances then relativity. It can get real messy, but Kip S. Thorne describes the entire process pretty well in his book Black Holes and Time Warps: Einstein's Outrageous Lagacy. It's about $15 American dollars, but I have yet to see references to quantum gravity with the detail he expresses anywhere else. I reccommend you buy the book or take it out of a local library.

: What are the most modern theories on what(and when)happens to energy(matter) at the singularity?