The general mechanism for photo-cross-linking of preformed polymers is studied by comparing the efficacy of monofunctional benzophenone (BP) and bifunctional bis-benzophenone (BP-BP) photoinitiators for inducing radical chain branching reactions in glassy polystyrene (PS) and rubbery poly(n-butyl acrylate) (PnBA). Upon UV irradiation, macroradicals form and initiate a variety of cross-linking and scission reactions. The kinetics and mechanisms of these macroradical reactions were monitored by gel permeation chromatography (GPC) measurements of changes in the polymer molecular weight distributions. Molecular weight increases are associated with chain branching while decreases in molecular weight are indicative of chain scission. We study the early stages of radical recombination where branching is manifest as the formation of three- and four-arm star polymers that are soluble and can be detected/differentiated by GPC. Branching is observed even in glassy PS; however, the reactions are much faster in rubbery PnBA, consistent with the expected influence of main chain mobility. At equal chromophore equivalents, BP-BP was found to be more efficient than BP for producing macroradicals, primarily due to a lower degree of self-quenching in BP-BP. When added to glassy PS, the higher efficiency of BP-BP did not translate into more chain branching, except at high additive concentration where the probability of BP-BP chain bridging reactions becomes significant, but instead led to a higher degree of main chain scission. The latter result was attributed to the larger distance between chromophores for BP-BP than for BP at equal benzophenone equivalents. In marked contrast, almost no main chain scission was found for either additive in PnBA, and BP-BP proved more effective for promoting chain branching. The susceptibility to main chain scission is found to be dependent upon the location of radical formation by hydrogen abstraction from the polymer. In PS, radicals can form on the chain backbone, and radical scission reactions lead to fragmentation of the polymer chain. In PnBA, radicals form preferentially on the pendant side chains, and radical scission reactions do not lead to main chain breakage. A simple probability-based model was found to capture the salient features of radiation-induced branching in preformed polymers.