A general methodology for solving the population balance equations for free-radical polymerization with long chain branching via chain transfer to polymer has been developed. The method calculates "instantaneous" molecular weight distributions for dead polymer species having i trifunctional branch points (where i=0,1,2,...) and monitors the consumption of chains and the distortion of these distributions by transfer to polymer during the course of the polymerization. The applicability of the method to isothermal batch polymerization for typical conditions in free-radical polymerization is demonstrated.