  Further improvements and refinements are brought to the microcanonical
multifragmentation model [Al. H. Raduta and Ad. R. Raduta, Phys. Rev. C {\bf
55}, 1344 (1997); {\it ibid.} {\bf 61}, 034611 (2000)]. The new version of the
model is tested on the recently published experimental data concerning the
Xe+Sn at 32 MeV/u and Gd+U at 36 MeV/u reactions. A remarkable good
simultaneous reproduction of fragment size observables and kinematic
observables is to be noticed. It is shown that the equilibrated source can be
unambiguously identified.
