The 31) bond fluctuation lattice model is extendedly developed to explore AB(n) (n = 2, 4) type hyperbranched polymerizations with the considerations of intramolecular rings, steric factors, diffusion of molecules, and polymer chain relaxation. In the case of zero activation energy, number- and weight-average degrees of polymerization and polydispersity index (PI) increase with the rise of monomer concentration and their maximal values are finite. The average fraction of branching point (FB), initially elevates with the increase of monomer concentration and then decreases at high concentration at full conversion of A groups. In the case of nonzero activation energy, the PI increases slowly with the decrease of reaction activity, but the average FB keeps nearly unchanging. The influence of substitution effect on PI and FB are also confirmed in simulation. The simulation results show excellent agreement with experimental data and are helpful to make great progress in prediction for AB(n) type hyperbranched polymerizations. (C) 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 523-533, 2009