The full molecular weight distribution formed in a batch free-radical copolymerization with chain transfer monomer is considered theoretically. A Monte Carlo simulation algorithm is proposed on the basis of the random sampling technique. Illustrative calculations are conducted for the cases with equal reactivity of all types of double bonds. It was found that even when the probability of possessing a branch point is the same for all units, the formed molecular weight distribution is highly dependent on the chain connection rule. Bimolecular termination by combination may contribute to form extremely large polymer molecules by forming cross-linkages between primary chains. Under the idealized conditions, homogeneously branched polymer molecules are formed, and the analytical solution for the molecular weight distribution can be obtained.