  We consider the problem of consumption of stars by a supermassive black hole
(SBH) at the center of an axisymmetric galaxy. Inside the SBH sphere of
influence, motion of stars in the mean field is regular and can be described
analytically in terms of three integrals of motion: the energy E, the
z-component of angular momentum L_z, and the secular Hamiltonian H. There exist
two classes of orbits, tubes and saucers; saucers occupy the
low-angular-momentum parts of phase space and their fraction is proportional to
the degree of flattening of the nucleus. Perturbations due to gravitational
encounters lead to diffusion of stars in integral space, which can be described
using the Fokker-Planck equation. We calculate the diffusion coefficients and
solve this equation in the two-dimensional phase space (L_z, H), for various
values of the capture radius and the degree of flattening. Capture rates are
found to be modestly higher than in the spherical case, up to a factor of a
few, and most captures take place from saucer orbits. We also carry out a set
of collisional N-body simulations to confirm the predictions of the
Fokker-Planck models. We discuss the implications of our results for rates of
tidal disruption and capture in the Milky Way and external galaxies.
