  This thesis embraces several aspects of theoretical stellar dynamics in
clusters, both analytically and numerically. We try to elucidate the phenomena
currently observed in all types of galaxies, including AGNs and quasars, some
of the most powerful objects in the universe. The interactions between the
stellar system and the central black hole give rise to a lot of interesting
phenomena. The scheme we employ enables a study of clean-cut aspects without
any noise that particle methods suffer from. We study the most important
physical processes that are readily available in the evolution of a spherical
cluster, like self-gravity, two-body relaxation etc, the interaction with a
central black hole and the role of a mass spectrum. Not only embark we upon
this subject, but we set about an analysis on super-massive stars. How these
stars could power the quasar activity by star accretion and energy flows is one
of the questions that arises. We undertake other questions, such as the
uncertain evolution of such an object and its interaction with the surrounding
stellar system. This is of crucial importance in astrophysics, for these
objects could be regarded as super-massive black holes progenitors.
