The preparation of hyperbranched polymers by the polymerization of monomers A(2) and B-3 with monofunctional monomers BR was investigated by recursive and kinetic models. A diagram of the gel and sol regions corresponding to the composition of the monomers was proposed. According to the kinetic model, the average degree of polymerization and the degree of branching (DB) that are dependent on the conversion and initial compositions of the reactants were calculated by a generating function method. If the molar ratio of B-3/A(2)/BR was 1:3:3, then polymers with a weight-average degree of polymerization of 171 and a DB of 0.97 could be obtained at a conversion of 0.99. Polyurethane acrylates were further prepared from various mixtures of trimethylolpropane ethoxylate (B-3), hexamethylene diisocyanate (A(2)), and hydroxyethyl acrylate (BR). The molecular weights of the polymers predicted by the model were in good agreement with those determined by gel permeation chromatography.