Hyperbranched polymers generated from the polymerization of AB(2)-type monomers and trifunctional cores with various reactivities were examined by means of the kinetic theory. The average molecular weight, polydispersity, degree of branching, and structural units of the hyperbranched polymers, which all changed with time or conversion, were calculated by a generating function method. Growth of the hyperbranched polymers was limited by adding C-3 monomers because no reactions occur among molecules with a core unit. The presence of multifunctional core monomers can reduce the polydispersity of the hyperbranched polymers but leads to less branching and more residual of unreacted core monomers. Increment of the reactivity of core monomers results in a lower weight-average degree of polymerization and a narrower molecular weight distribution of the hyperbranched polymers.