A novel synthetic procedure for the preparation of hyperbranched polymers with narrow molecular weight distribution and enhanced degree of branching (DB) has been studied, using computer simulation to model the kinetics of the process. Slow addition of AB(m) monomers to B(f) core molecules in solution ("core-dilution/slow addition technique") can be used to prepare hyperbranched polymers in a controlled manner, provided the coupling reaction B(f) + AB(m) to B(f+m-1) is rapid and quantitative. The computer simulation is based on random addition of AB, monomers to B-functionalities of the B(f) core molecules for m = 2, 3 and f ranging from 2 to 12, excluding sterical constraints. It is shown that this synthetic strategy permits one to (i) control molecular weights, (ii) lower polydispersity, and (iii) enhance the DB of the resulting hyperbranched polymers. In the ideal case (AB, molecules react only with core B-functionalities and not with other AB(m) monomers) narrow molecular weight distributions are obtained, ranging from M(w)/M(n) = 1.33 to 1.08 for f = 3 and f = 12, respectively; i.e., polydispersities are controlled by the core functionality f. Obviously, for m = 2 the polydispersity for the core-dilution/slow addition process obeys the expression M(w)/M(n), = 1 + 1/f. The DB obtained from the simulation is 2/3 for m = 2 and 3/5 for m = 3, in excellent agreement with recent theoretical predictions, showing that DB = m/(2m - 1) for slow addition of AB, monomers (Acta Polym. 1997, 48, 298). Also, the nonideal case is considered, when AB(m) monomers form new core molecules B(m) in the course of the reaction due to deactivation of the reactive A-function. In this case bimodal distributions are obtained.