The unified analytical expressions of the size distribution function and the degree of branching for the hyperbranched polymerization with ABg type monomers are developed by kinetic theory of polymerization, based on the ABg + ABh + Bf model. The effect of the reactant parameters, the monomers branching degree g and h, the monomers feed ratio r, the functionality f and feed ratio α of the core molecule Bf, on the molecular parameters of the products formed was investigated. Compared with the general polycondensation of ABg monomer or copolycondensation of ABg and AB monomer without core molecule, the presence of multifunctional core molecules makes the polydispersity index of the products go down fast when the reaction approaches completion. At the end of the reaction, the polydispersity index increases with increasing g, and decreases with increasing α and f. For the ABg + AB + B3 polycondensation system, within the range of the feed ratio of ABg monomer less than 0.3, the average chain segment length significantly decreases with the increasing r, and then the change becomes moderate with its further increase. For g > 2, the average chain segment length shows a shallow minimum with increasing r. The degree of branching, fractions of terminal and branching units also show maximum value with the change of monomer feed ratio r. The information obtained in this work can help people understand the structure of ABg type hyperbranched polymers and carry out molecular design.