We report Monte Carlo simulations of chemical potentials on short ranging primitive models (PM) of water due to Nezbeda and co-workers. Since Widom's test particle method fails for network forming PM water, we simulate chemical potentials by gradual particle insertion. From chemical potential versus packing fraction isotherms, we estimate densities of coexisting phases by means of a Maxwell equal-area rule. Site-site correlation functions, cluster size distributions, and mean square displacements of coexisting phases are analysed. The presented chemical potentials and coexistence properties should be considered as important reference data for PM based molecular theories of associating fluids. (C) 2003 Elsevier B.V. All rights reserved.