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We consider the problem of distributing a content of finite size to a group of users connected through an overlay network that is built by a peer-to-peer application. The goal is the fastest possible diffusion of the content until it reaches all the peers. Applications like Bit-Torrent or SplitStream are examples where the problem we study is of great interest. In order to represent the content diffusion process, we model the system as a stochastic graph process and define the constraints the graph evolution is subject to. The evolution of the graph is a semi-Markov process where the sojourn times are the rewards of interest for the computation of the time needed to complete the file distribution. We discuss the general properties of the constrained stochastic graphs and we show preliminary results obtained with an ad-hoc Monte-Carlo technique.