  An exact analytical solution of the statistical multifragmentation model is
found in thermodynamic limit. The model exhibits a 1-st order phase transition
of the liquid-gas type. The mixed phase region of the phase diagram, where the
gas of nuclear fragments coexists with the infinite liquid condensate, is
unambiguously identified. The peculiar thermodynamic properties of the model
near the boundary between the mixed phase and the pure gaseous phase are
studied. The results for the caloric curve and specific heat are presented and
a physical picture of the nuclear liquid-gas phase transition is clarified.
