This work theoretically deals with the kinetics of the co-polycondensation of AB(2) and AB type monomers in the presence of multi-functional cores. The analytical expressions of the molecular size distribution function and the molecular parameters of the resultant hyperbranched polymers were derived. The general expressions are applicable for the copolymerization of AB(2) and AB monomers and the polymerization of homogeneous AB(2) or AB monomers in either presence or absence of cores. The feed ratio of the core molecules (beta) or the AB(2) monomers (alpha) to the total monomers significantly affects the molecular weight distribution and the molecular parameters of the products. The polydispersity index of the copolymerization of AB(2) and AB monomers without cores is infinite when the reaction approaches to completion, while the presence of core molecules makes it become finite. The polydispersity index decreases with decreasing a, which also decreases with increasing beta. The higher the functionality of the core (f), the lower the polydispersity index is as well. (c) 2010 Elsevier Ltd. All rights reserved.