AbstractA general kinetic analysis of the polymerization of a monomer in the presence of a pre‐formed polymer having chain transfer sites of high activity is presented. Equations are given predicting both the grafting efficiency and the molecular weights of interest. Most of the results are expressed in terms of definite integrals which, except for special values of C8, require numerical evaluation. In most cases, approximate closed form equations can be used. The results are expressed in terms of the polymerization constants of the monomer, the initial rate of polymerization, the fractional conversion to polymer, and the decrease in the concentration of transfer sites.