  To be presented is a study of the secular evolution of a spherical stellar
system with a central star-accreting black hole (BH) using the anisotropic
gaseous model. This method solves numerically moment equations of the full
Fokker-Planck equation, with Boltzmann-Vlasov terms on the left- and
collisional terms on the right-hand sides. We study the growth of the central
BH due to star accretion at its tidal radius and the feedback of this process
on to the core collapse as well as the post-collapse evolution of the
surrounding stellar cluster in a self-consistent manner. Diffusion in velocity
space into the loss-cone is approximated by a simple model. The results show
that the self-regulated growth of the BH reaches a certain fraction of the
total mass cluster and agree with other methods. Our approach is much faster
than competing ones (Monte Carlo, $N$--body) and provides detailed informations
about the time and space dependent evolution of all relevant properties of the
system. In this work we present the method and study simple models (equal
stellar masses, no stellar evolution or collisions). Nonetheless, a
generalisation to include such effects is conceptually simple and under way.
