  A two dimensional self-gravitating Hamiltonian model made by $N$
fully-coupled classical particles exhibits a transition from a collapsing phase
(CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical
point of view, the two phases are characterized by two distinct single-particle
motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous
diffusion is observed up to a time $\tau$ that increases linearly with $N$.
Therefore, the finite particle number acts like a white noise source for the
system, inhibiting anomalous transport at longer times.
