  We show that the self-gravitating gas at thermal equilibrium has an infinite
volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty,
keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We
develop MonteCarlo simulations, analytic mean field methods (MF) and low
density expansions. We compute the equation of state and find it to be locally
p(r) = T rho_V(r), that is a local ideal gas equation of state. The system is
in a gaseous phase for eta < eta_T = 1.51024...and collapses into a very dense
object for eta > eta_T in the CE with the pressure becoming large and negative.
The isothermal compressibility diverges at eta = eta_T. We compute the
fluctuations around mean field for the three ensembles. We show that the
particle distribution can be described by a Haussdorf dimension 1 < D < 3.
