  The microcanonical properties of a two dimensional system of N classical
particles interacting via a smoothed Newtonian potential as a function of the
total energy E and the total angular momentum L are discussed. In order to
estimate suitable observables a numerical method based on an importance
sampling algorithm is presented. The entropy surface shows a negative specific
heat region at fixed L for all L. Observables probing the average mass
distribution are used to understand the link between thermostatistical
properties and the spatial distribution of particles. In order to define a
phase in non-extensive system we introduce a more general observable than the
one proposed by Gross and Votyakov [Eur. Phys. J. B:15, 115 (2000)]: the sign
of the largest eigenvalue of the entropy surface curvature. At large E the
gravitational system is in a homogeneous gas phase. At low E there are several
collapse phases; at L=0 there is a single cluster phase and for L>0 there are
several phases with 2 clusters. All these pure phases are separated by first
order phase transition regions. The signal of critical behaviour emerges at
different points of the parameter space (E,L). We also discuss the ensemble
introduced in a recent pre-print by Klinko & Miller; this ensemble is the
canonical analogue of the one at constant energy and constant angular momentum.
We show that a huge loss of informations appears if we treat the system as a
function of intensive parameters: besides the known non-equivalence at first
order phase transitions, there exit in the microcanonical ensemble some values
of the temperature and the angular velocity for which the corresponding
canonical ensemble does not exist, i.e. the partition sum diverges.
