  Purely self-gravitating systems of point particles have been extensively
studied in astrophysics and cosmology, mainly through numerical simulations,
but understanding of their dynamics still remains extremely limited. We
describe here results of a detailed study of a simple class of cold
quasi-uniform initial conditions, for both finite open systems and infinite
systems. These examples illustrate well the qualitative features of the quite
different dynamics observed in each case, and also clarify the relation between
them. In the finite case our study highlights the potential importance of
energy and mass ejection prior to virialization, a phenomenon which has been
previously overlooked. We discuss in both cases the validity of a mean-field
Vlasov-Poisson description of the dynamics observed, and specifically the
question of how particle number should be extrapolated to test for it.
