This paper developed a kinetic model for the polycondensation of ABg type monomers with a multifunctional core (RBf), giving the expressions of the molecular weight distribution function and average molecular weights of the resulting hyperbranched polymers. During the polycondensation both g and f markedly influence on the width of the molecular weight distribution of the products. When the reaction approaches completion, the molecular weight distribution of the resultant polymers is found to broaden with increasing g, and become narrower with increasing f. Hence the effect of increasing g on the polydispersity index can be offset by increasing f. (C) 2000 Elsevier Science Ltd. All rights reserved.