  We study the process of spinning up black holes by accretion from slim disks
in a wide range of accretion rates. We show that for super-Eddington accretion
rates and low values of the viscosity parameter alpha (\lesssim 0.01) the
limiting value of the dimensionless spin parameter a_* can reach values higher
than a_*=0.9978 inferred by Thorne (1974) in his seminal study. For
\mdot=10\mdot_{Edd} and alpha=0.01 spin equilibrium is reached at a_*=0.9994.
We show that the equilibrium spin value depends strongly on the assumed value
of alpha. We also prove that for high accretion rates the impact of captured
radiation on spin evolution is negligible.
