This work reports a kinetic model developed to provide insight into branching mechanisms and control of gelation by semibatch controlled radical copolymerization processes. The semibatch RAFT copolymerization of acrylamide (AM) and N,N'-methylenebis(acrylamide) (BisAM) in the presence of 3-benzyltrithiocarbonyl propionic acid (BCPA) as chain transfer agent (CTA) was carried out for the model validation. The BisAM was fed to the reactor at a constant rate to yield hyperbranched polyacrylamide (b-PAM) without gelation. Different feeding rates and [BisAM](0)/[CTA](0) ratios were theoretically simulated and experimentally investigated to optimize the instantaneous BisAM concentration in the reactor for branching formations. No gel was formed in the semibatch operation up to 99% total monomer conversion, in contrast to gel occurrence at 70% conversion in its corresponding batch operation. The polymer molecular weight and polydispersity as well as branching density increased slowly throughout the semibatch polymerization. Cyclization reactions were significant and helped to suppress the gelation. The model simulations correlated the experimental data very well.