The phase behavior of charge- and size-asymmetric primitive model electrolytes has been investigated using reservoir grand canonical Monte Carlo simulations. The simulations rely on the insertion and removal of neutral ion clusters from a reservoir of possible configurations. We first validated our approach by investigating the effect of R-c, the maximum allowable distance between the central cation and its associated anions, on the critical parameters of 2:1 and 3:1 electrolytes. We have shown that the effect of R-c is weak and does not change the qualitative dependence of the critical parameters on size and charge asymmetry. The critical temperature for 2:1 and 3:1 electrolytes shows a maximum at R(c)approximate to3, while the critical volume fraction decreases more or less monotonically, consistent with previous results for 1:1 electrolytes by Romero-Enrique [Phys. Rev. E 66, 041204 (2002)]. We have used the reservoir method to obtain the critical parameters for 5:1 and 10:1 electrolytes. The critical temperature decreases with increasing charge asymmetry and shows a maximum as a function of delta, the size asymmetry parameter. The critical volume fraction however, defined as the volume occupied by ions divided by the total volume of the simulation box, increases with increasing charge asymmetry and exhibits a minimum as a function of delta. This trend is contrary to what is generally predicted by theories, although more recent approaches based on the Debye-Huckel theory reproduce this observed trend. Our results deviate somewhat from the predictions of Linse [Philos. Trans. R. Soc. London, Ser. A 359, 853 (2001)] for the scaling of the critical temperature for a system of macroions with point counterions. (C) 2003 American Institute of Physics.