Applying advanced statistical techniques, we characterize the peculiarities of a locally observed peer population in a popular P2P overlay network. The latter is derived from a mesh-pull architecture. Using flow data collected at a single peer, we show how Pareto and Generalized Pareto models can be applied to classify the local behavior of the population feeding a peer. Our approach is illustrated both by file sharing data of a P2P session generated by a mobile BitTorrent client in a WiMAX testbed and by video data streamed to a stationary client in a SopCast session. These techniques can help us to cope with an efficient adaptation of P2P dissemination protocols to mobile environments.