Irreversible non-linear copolymerizations with arbitrarily great numbers of monomers are described specifying the stoichiometric coefficients of the reactions involving end-groups. Rate equations for the vectorial generating function or discrete transform of the distribution of end-groups and repeating units and its derivatives with respect to logarithms of Laplace parameters can thus be written. Similar rate equations can be written for the discrete transforms of the distributions of descendants of each linking group with respect to their numbers of end-groups. This allows the prediction of gel properties, such as the concentration of elastically active network chains and mass fraction of pendant material. Mass balance equations using these rate laws are non-linear partial differential equations solvable by the method of characteristics. Numerical methods are developed for computing molecular weight distributions and average molecular weights before and after gelation, as well as the weight fraction of sol and gel properties related to its elasticity behaviour. The curing of a tetraepoxide with a primary diamine is taken as a case study and results are compared with predictions by the theory of branching processes.