  (Context) In a Universe dominated by dark matter, halos are continuously
accreting mass (violently or not) and such mechanism affects their dynamical
state. (Aims) The evolution of dark matter halos in phase-space, and using the
phase-space density indicator Q=rho/sigma^3 as a tracer, is discussed.
(Methods) We have performed cosmological N-body simulations from which we have
carried a detailed study of the evolution of ~35 dark halos in the interval
0<z<10. (Results)The follow up of individual halos indicates two distinct
evolutionary phases. First, an early and fast decrease of Q associated to
virialization after the gravitational collapse takes place. The nice agreement
between simulated data and theoretical expectations based on the spherical
collapse model support such a conjecture. The late and long period where a slow
decrease of the phase-space density occurs is related to accretion and merger
episodes. The study of some merger events in the phase-space (radial velocity
versus radial distance) reveals the formation of structures quite similar to
caustics generated in secondary infall models of halo formation. After mixing
in phase-space, halos in quasi-equilibrium have flat-topped velocity
distributions (negative kurtosis) with respect to Gaussians. The effect is more
noticiable for captured satellites and/or substructures than for the host halo.
