Lattice Monte Carlo simulation is used to study micellization of both pure and surfactant-polymer mixture, with an emphasis on cluster size distribution. The amphiphile molecule is of the type H(4)T(4) where the H (head) monomers like the solvent molecules and the T (tail) monomers are solvophobic. To compare polymer- and surfactant-centered theories, copolymers with the structure of (H(4)T(4))(5) are used instead of homopolymers. Since above copolymer molecules have the structural unit like the structure of surfactant molecules, it is possible to study the competition between the binding of surfactant molecules to the copolymer and the micellization in a copolymer-free solution. Results show that, first, surfactant molecules bind to the copolymer molecules, and not until copolymers are saturated do micelles form. Furthermore, it is shown that for the model used in this paper, the polymer-centered theory is more appropriate than the surfactant-centered theory, and finally the cooperative nature of cluster formation on copolymers is also discussed.