This paper is a short summary of the main results in the thesis . Based on the P2P paradigm we construct a stochastic model for a live media streaming content delivery network. Starting from the behavior of the out degree process of each node we analyze the evolution of the resulting random graph. For the out degree process we provide an iterative formula for the distribution probabilities and calculate an explicit expression for the transient distribution. Moreover we discuss the steady state distribution and the problem of local disconnections.