  We use numerical simulations to investigate the cusp at the centre of
elliptical galaxies, due to the slow growth of a super-massive black hole. We
study this problem for axisymmetric models of galaxies, with or without
rotation. The numerical simulations are based on the `Perturbation Particles'
method, and use GRAPEs to compute the force due to the cusp. We study how the
density cusp is affected by the initial flattening of the model, as well as the
role played by initial rotation. The logarithmic slope of the density cusp is
found to be very much insensitive to flattening; as a consequence, we deduce
that tangential velocity anisotropy -which supports the flattening- is also of
little influence on the final cusp. We investigate via two different kinds of
rotating models the efficiency with which a rotation velocity component builds
within the cusp. A cusp in rotation develops only for models where a net
rotation component is initially present at high energy levels. The eventual
observation of a central rotational velocity peak in E galaxies has therefore
some implications for the galaxy dynamical history.
