  The thermodynamical cluster model is known to present a first-order
liquid-gas phase transition in the idealized case of an uncharged, infinitely
extended medium. However, in most practical applications of this model, the
system is finite and charged. In this paper we study how the phase diagram is
modified by finite size and Coulomb effects.
  We show that the thermodynamic anomalies which are associated to the finite
system counterpart of first order phase transitions, are correctly reproduced
by this effective model. However, approximations in the calculation of the
grandcanonical partition sum prevent obtaining the exact mapping between
statistical ensembles which should be associated to finite systems. The
ensemble inequivalence associated to the transition persists in the presence of
Coulomb, but the phase diagram is deeply modified with respect to the simple
liquid-gas phase transition characteristic of the neutral system.
