  Simulations in general relativity show that the outcome of collapse of a
marginally unstable, uniformly rotating star spinning at the mass-shedding
limit depends critically on the equation of state. For a very stiff equation of
state, which is likely to characterize a neutron star, essentially all of the
mass and angular momentum of the progenitor are swallowed by the Kerr black
hole formed during the collapse, leaving nearly no residual gas to form a disk.
For a soft equation of state with an adiabatic index \Gamma - 4/3 << 1, which
characterizes a very massive or supermassive star supported predominantly by
thermal radiation pressure, as much as 10% of the mass of the progenitor avoids
capture and goes into a disk about the central hole. We present a semi-analytic
calculation that corroborates these numerical findings and shows how the final
outcome of such a collapse may be determined from simple physical
considerations. In particular, we employ a simple energy variational principle
with an approximate, post-Newtonian energy functional to determine the
structure of a uniformly rotating, polytropic star at the onset of collapse as
a function of polytropic index n, where \Gamma = 1+1/n. We then use this data
to calculate the mass and spin of the final black hole and ambient disk. We
show that the fraction of the total mass that remains in the disk falls off
sharply as 3-n (equivalently, \Gamma - 4/3) increases.
