The statistical method was used to give the number of bonds formed for the star-branched polymer chains made by the AB + A(f) polymerization. On the basis of the kinetic model described by the Smoluchowski-like coagulation equation, the mean-square radii of gyration were given analytically. Furthermore, the z- and weight-average mean-square radii of gyration were investigated explicitly. The results were much different from that of the hyperbranched polymers made by the AB(f) type monomers, where the former had the finite values when the reaction was quantitatively completed, and the latter reached the infinite values. In principle, by varying the number of the Af type multifunctional core moieties, the average sizes, as well as the average degrees, can be controlled effectively.