Code mobility and mobile agents have received a lot of attention as a paradigm based on which distributed applications can be built. There has been little work however on the mathematical modeling of component mobility. In this direction, we present and analyze three optimization models for component mobility. We are seeking the optimal allocation of components to network nodes and the optimal component routes that will minimize the network traffic that is incurred in the course of component communication. Optimal solutions are found either through a mixed binary integer programming formulation or by employing max flow computations. Complexity results are also reported.