This work is theoretically dealt with the kinetics of polycondensation of AB(2)-type monomers in the presence of multifunctional cores (C-f) with various reactivities. The analytical expressions of the molecular size distribution function and the molecular parameters of the resultant hyperbranched polymers were derived. The conversion of A groups (x), feed ratio of the core/monomer (beta), functionality of the core (f), and reactivity ratio of C to B (r) significantly effect the molecular weight distribution and the molecular parameters of the products. High feed ratio, functionality and reactivity of the core can improve the molecular weight distribution and decrease the polydispersity for the resultant products. Compared with the polycondensation of equal reactivity, the effect of the core which has enough high reactivity on the polydispersity is equal to doubling the functionality of the core. (c) 2012 Elsevier Ltd. All rights reserved.