N-body realizations of axisymmetric collisional galaxy cores (e.g. M32, M33, NGC 205, Milky Way) with embedded growing black holes are presented. Stars which approach the disruption sphere are disrupted and accreted to the black hole. We measure the zone of influence of the black hole and disruption rates in relaxation time-scales. We show that secular gravitational instabilities dominate the initial core dynamics, while the black hole is small and growing due to the consumption of stars. Later, the black hole potential dominates the core, and the loss cone theory can be applied. Our simulations show that central rotation in galaxies cannot be neglected for relaxed systems, and compare and discuss our results with the standard theory of spherically symmetric systems.