The number of the hyperbranched polymers in the system is investigated for the polymerization process to give the asymptotic form of the concentration of the n-mer. The polydispersity exponent is calculated, which coincides with that of the classical result. Finally, the asymptotic forms of the number, the weight and the z-average degrees of the polymerization were evaluated analytically to obtain polydispersity index, which is close to 1 as the reaction is quantitatively completed. The number of the hyperbranched polymers in the system is investigated for the polymerization process to give the asymptotic form of the concentration of the n-mer. The polydispersity exponent is calculated, which coincides with that of the classical result. Finally, the asymptotic forms of the number, the weight and the z-average degrees of the polymerization were evaluated analytically to obtain a polydispersity index, which is close to 1 as the reaction is quantitatively completed.