  We present a numerical study of the non-equilibrium dynamics of the
Sherrington-Kirkpatrick model. We analize the overlap distribution between the
configurations visited at the time t and in particular its scaling behaviour
with the size of the system. We find two different non-equilibrium dynamical
regimes. The first is a proper Out of Equilibrium Regime, that is the relevant
regime for the dynamics of an infinite system. The second is an Intermediate
Regime that separates the Out of Equilibrium Regime from equilibrium. After
studying the crossover beetween the two regimes, we focus on the Out of
Equilibrium Regime and we reveal some of the geometrical features of phase
space. According to recent analitical work, we find that the asymptotic out of
equilibrium energy density is the equilibrium one. The same happens to the
staggered-magnetisation, suggesting there is a deep geometrical similarity
between equilibrium and out of equilibrium configurations. A procedure, that we
call clonation, shows that the dynamics follows sort of canyons, as opposed to
a system of independent traps.
