We consider the stellar-dynamical processes which lead to
the capture or tidal disruption of stars by a supermassive black hole, review
the standard theory of two-body relaxation and loss-cone repopulation in
spherical galactic nuclei, and extend it to the axisymmetric and triaxial
nuclear star clusters.
In the absense of symmetry which conserves angular
momentum, the orbits of stars experience regular or chaotic changes of angular
momentum even in the smooth potential of star cluster, which creates a substantial
population of "centrophilic" orbits. We discuss the loss cone
draining rates, i.e. rates of capture of stars from these orbits.
Next we consider the relaxation phenomena in
non-spherical nuclei, focusing on the differences between spherical, axisymmetric
and triaxial cases. It turns out that the rates of repopulation of the loss
cone are moderately higher in non-spherical systems, but in the triaxial case
an additional, often substantial, increase of capture rates comes from draining
of the centrophilic orbit population.