The pregelation weight-average molecular weights of cross-linked polymers and silica-based sol-gels diverge at the sol-gel transition, where time t approaches the gel time t(c). The divergence follows a power law, (1 - t/t(c))(-gamma), with a critical exponent larger than the gamma = 1 prediction of classic Flory-Stockmayer er theory and of our previous cross-linking model. In this paper we modify the cross-linking mechanism by allowing a fractional exponent, 0 < omega <= 1, for the mass-dependent rate kernel to match the critical exponents of real systems. Moment equations solved by closure approximations show that gamma is determined solely by omega, in agreement with an existing analytical solution. The rate constants for crosslinking, addition, and condensation polymerization have essentially no effect on gamma. We also obtained for the first time an analytical expression for gel time, in agreement with moment closure solutions for values of omega other than 0 or 1. When omega is either 3/4 or 5/6, good approximations to experimental values of gamma for silica sol-gel or polymer, respectively, are found.