  The collapse of a uniformaly rotating, supermassive star (SMS) to a
supermassive black hole (SMBH) has been followed recently by means of
hydrodynamic simulations in full general relativity. The initial SMS of
arbitrary mass M in these simulations rotates uniformly at the mass--shedding
limit and is marginally unstable to radial collapse. The final black hole has
mass M_h/M = 0.9 and and spin J_h/M_h^2 = 0.75, approximately. The remaining
mass goes into a disk of mass M_disk/M = 0.1, also approximately. Here we show
that these black hole and disk parameters can be calculated analytically from
the initial stellar density and angular momentum distribution. The analytic
calculation thereby corroborates and provides a simple physical explanation for
the computational discovery that SMS collapse inevitably terminates in the
simultaneous formation of a SMBH and a rather substantial ambient disk. This
disk arises even though the total spin of the progenitor star, J/M^2 = 0.97, is
safely below the Kerr limit. The calculation performed here applies to any
marginally unstable n = 3 polytrope uniformly rotating at the break--up speed,
independent of stellar mass or the source of internal pressure. It illustrates
how the black hole and disk parameters can be determined for the collapse of
other types of stars with different initial density and rotation profiles.
