The molecular weight distribution and its moments for the hyperbranched polymer formed by the polycondensation of an AB(2) type monomer with a multifunctional core moiety were derived rigorously by means of the kinetic method. The variations of several molecular parameters of the growing polymer during the reaction were estimated. The presence of a small amount of multifunctional core molecules, RBf, in the polycondensation system of AB(2) type monomers is found to lead to a marked reduction in the polydispersity index of the final polymer. During the polymerization process, the molecular weight distribution first becomes broader with increasing conversion of A groups and then abruptly becomes considerably more narrow as the reaction approaches completion. The greater the number of functional groups in the core moiety, the narrower the final molecular weight distribution of the polymer.