Naive reading on the web says that stellar collapse is halted by quantum mechanical processes called "degenerate pressures" that arise when gravity tries to force fermions such as electrons or neutrons into the same quantum state. White dwarfs are propped up by electrons, neutron stars by neutrons, and it is speculated that other quantum mechanical plasmas may stabilize larger collapsing stars e.g quark plasmas. See for instance the Wikipedia articles on White Dwarfs and Neutron Stars. Also the Hubble telescope seems to have detected evidence of an anomalous neutron star that might really be a quark star. From this it seems that matter tries to do its best to resist gravitational crunch but at some point gives up the battle. Why is this? Is it that beyond a certain limit there are no longer any more types of elementary particles that can counter stellar collapse? Or is is just that no matter what goes on in the quantum world General Relativity says a singularity is inevitable if the collapsing star is big enough? It seems a bit peculiar that Relativity predicts a singularity without any reference whatsoever to these quantum pressures. Finally, as the singularity forms what happens to matter on its way down? Does it go through a series of stages of attempted resistance first say forming an electron plasma , then a neutron, then perhaps a quark and then others or is the process completely different?