  We have recently written a new code to simulate the long term evolution of
spherical clusters of stars. It is based on the pioneering Monte Carlo scheme
proposed by Henon in the 70's. Our code has been devised in the specific goal
to treat dense galactic nuclei. After having described how we treat relaxation
in a first paper, we go on and include further physical ingredients that are
mostly pertinent to galactic nuclei, namely the presence of a central (growing)
black hole (BH) and collisions between MS stars. Stars that venture too close
to the BH are destroyed by the tidal field. This process is a channel to feed
the BH and a way to produce accretion flares. Collisions between stars have
often been proposed as another mechanism to drive stellar matter into the
central BH. To get the best handle on the role of this process in galactic
nuclei, we include it with unpreceded realism through the use of a set of more
than 10000 collision simulations carried out with a SPH (Smoothed Particle
Hydrodynamics) code. Stellar evolution has also been introduced in a simple
way, similar to what has been done in previous dynamical simulations of
galactic nuclei. To ensure that this physics is correctly simulated, we
realized a variety of tests whose results are reported here. This unique code,
featuring most important physical processes, allows million particle
simulations, spanning a Hubble time, in a few CPU days on standard personal
computers and provides a wealth of data only rivalized by N-body simulations.
