  We estimate the rate at which stars are captured by supermassive black holes
(BHs) in the centres of bulges and elliptical galaxies assuming that these
initially had an isothermal cusp (rho ~ r^{-2} with velocity dispersion
sigma_*). If radial orbits can be adequately replenished a BH can grow
significantly by capturing stars and particles of the dark halo; the latter
could be up to 20--40 percent of the total mass captured. A tight relation M_bh
10^8 (sigma_*/200\kms)^5 between BH hole mass and stellar velocity dispersion
arises at the high mass end M_bh >= 10^8 M_sun if these giant BHs grow
primarily by swallowing stars. For smaller masses a gradual flattening of the
relation and an increase of the scatter are expected due to tidal disruption of
stars. At moderate redshifts when bright galaxies may still possess isothermal
cusps tidal disruption flares may be as frequent as 10^{-4} -- 10^{-2} yr^{-1}
per galaxy, a few percent of the supernovae rate. Efficient randomization of
the orbits can occur when the dense cores of infalling satellites sink to the
sphere of influence of the BH by dynamical friction. Efficient replenishment of
the loss cone of radial orbits can also explain why the supermassive binary BHs
expected in hierarchically merging galaxies do generally coalesce, as suggested
by the observed relation between BH mass and the inferred mass of stars ejected
from an isothermal cusp.
