  We calculate the structure of accretion disks around Kerr black holes for
accretion rates 0.001 - 10 M_sun/s. Such disks are plausible candidates for the
central engine of gamma-ray bursts. Our disk model is fully relativistic and
treats accurately microphysics of the accreting matter: neutrino emissivity,
opacity, electron degeneracy, and nuclear composition. The neutrino-cooled disk
forms above a critical accretion rate that depends on the black hole spin. The
disk has the ``ignition'' radius r_ign where neutrino flux rises dramatically,
cooling becomes efficient, and the proton-to-nucleon ratio Y_e drops. Other
characteristic radii are r_alpha where most of alpha-particles are
disintegrated, r_nu where the disk becomes neutrino-opaque, and r_trap where
neutrinos get trapped and advected into the black hole. We find r_alpha, r_ign,
r_nu, r_trap and show their dependence on the accretion rate. We discuss the
qualitative picture of accretion and present sample numerical models of the
disk structure. All neutrino-cooled disks regulate themselves to a
characteristic state such that: (1) electrons are mildly degenerate, (2) Y_e ~
0.1, and (3) neutrons dominate the pressure in the disk.
