  We study, using both theory and molecular dynamics simulations, the
relaxation dynamics of a microcanonical two dimensional self-gravitating
system. After a sufficiently large time, a gravitational cluster of N particles
relaxes to the Maxwell-Boltzmann distribution. The time to reach the
thermodynamic equilibrium, however, scales with the number of particles. In the
thermodynamic limit, $N\to\infty$ at fixed total mass, equilibrium state is
never reached and the system becomes trapped in a non-ergodic stationary state.
An analytical theory is presented which allows us to quantitatively described
this final stationary state, without any adjustable parameters.
