Theory and simulations are used to study collisionless relaxation of a
gravitational N-body system. It is shown that when the initial one particle
distribution function satisfies the virial condition -- potential energy is
minus twice the kinetic energy -- the system quickly relaxes to a metastable
state described {\it quantitatively} by the Lynden-Bell distribution with a
cutoff. If the initial distribution function does not meet the virial
requirement, the system undergoes violent oscillations, resulting in a partial
evaporation of mass. The leftover particles phase separate into a core-halo
structure. The theory presented allows us to quantitatively predict the amount
and the distribution of mass left in the central core, without any adjustable
parameters. On a longer time scale τG​∼N collisionless relaxation
leads to a gravothermal collapse