  In this paper, we present our conclusions from the numerical study of the
collapse of a destabilized collisionless stellar system. We use both direct
integration of the Vlasov-Poisson equations and an N-body tree code to obtain
our results, which are mutually confirmed. We find that spherical and
moderately nonspherical collapse configurations evolve to new equilibrium
configurations in which the velocity distribution approaches a Gaussian form,
at least in the central regions. The evolution to this state has long been an
open question, and in this work we are able to clarify the process responsible
and to support predictions made from statistical considerations (Lynden-Bell
1967; Nakamura 2000). The simulations of merging N-body systems show a
transition to a Gaussian velocity distribution that is increasingly suppressed
as the initial separation of centres is increased. Possible reasons for this
are discussed.
