  We study gravitational collapse of rapidly rotating relativistic polytropes
of the adiabatic index $\Gamma = 1.5$ and 2, in which the spin parameter $q
\equiv J/M^{2} > 1$ where $J$ and $M$ are total angular momentum and
gravitational mass, in full general relativity.
  First, analyzing initial distributions of the mass and the spin parameter
inside stars, we predict the final outcome after the collapse. Then, we perform
fully general relativistic simulations on assumption of axial and equatorial
symmetries and confirm our predictions. As a result of simulations, we find
that in contrast with the previous belief, even for stars with $q > 1$, the
collapse proceeds to form a seed black hole at central region, and the seed
black hole subsequently grows as the ambient fluids accrete onto it. We also
find that growth of angular momentum and mass of the seed black hole can be
approximately determined from the initial profiles of the density and the
specific angular momentum. We define an effective spin parameter at the central
region of the stars, $q_{c}$, and propose a new criterion for black hole
formation as $q_{c} \alt 1$. Plausible reasons for the discrepancy between our
and previous results are clarified.
