Synthesis and characterization of tightly branched, rigid, network polymers based on the cyanate functional group are reported. Monofunctional model compound 2-(4-cyanatophenyl)-2-phenylpropane (CPP) was reacted in bulk to establish the reaction chemistry. It is found that trimerization which forms the cyclic triazine ring is the dominant reaction occurring in excess of 90%. Polymers based on the bifunctional compound 2,2-bis(4-cyanatophenyl)propane (BCP) were synthesized thermally in bulk without a catalyst. Number-average molecular weight (from 13C NMR and SEC) and weight-average molecular weight (from SEC) are reported as a function of cyanate group conversion (from 13C NMR and IR). The gel conversion is found to be over 60%, significantly higher than the mean-field value of 50%. The source of this disagreement is discussed. Gel conversion of polymers based on the combinations of CPP and BCP is closer to the mean-field value with increasing CPP in the initial stoichiometry. One explanation which is consistent with all experimental results is that the growth of rigid polycyanate networks is controlled by the accessibility of functional groups. The experimental results point to the limitations of mean-field theory. The nature of these limitations is explored through Monte Carlo simulations.