Graft site initiation occurs by primary radical and/or polymeric radical attack on the backbone polymer. The controlling mechanism is determined by the structure of the backbone and the activity of the free radicals. The efficiency of incorporating monomer into the graft chains depends upon the graft site initiation mechanism and the mode of polymer chain termination (recombination or disproportionation). A kinetic analysis results a series of uniquely different expressions describing the graft efficiency, phi, corresponding to different combinations of graft site initiation and chain termination mechanisms. The dependency of phi upon monomer, initiator, and backbone concentrations is different from case to case. The complete kinetic model is capable of predicting reaction rate, graft efficiency, graft frequency, graft ratio, and molecular weight averages and distributions. Simulations are provided to compare predicted results with experimental data for two different systems which show contrasting mechanisms of graft site initiation and mode of termination.