A lattice model has been utilized to calculate the free energy change upon oligomeric radical (derived from persulfate initiators) adsorption onto a latex particle dispersed in an aqueous phase. Variations in this free energy change with oligomer chain length allow one to predict the so-called Z-mer length at which adsorption is spontaneous. Z-mer lengths for commonly used homopolymers range from 1 to 8 (for 2-ethylhexyl acrylate and methyl acrylate, respectively). The lengths predicted for styrene and methyl methacrylate are 2 and 4 and are the same as those reported from experiments. The model is straightforwardly extended to copolymers. Here the overall composition of the oligomeric copolymer radical has a significant effect upon the Z-mer length, while the sequence distribution of the monomer units in the chain has a limited effect. Model predictions for the acrylic acid-styrene system are in reasonable agreement with reported experimental results over a range of comonomer compositions.