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This work presents a study on the fault-tolerance of unstructured P2P overlays, modeled as complex networks. A framework is proposed to derive the peers' degree distribution, once the P2P system is described through the evolution laws characterizing the distributed protocol, the attachment and failure rates. From the degree distribution, estimations may be derived on the mean number of m-neighbors, as well as the diameter of the net. We analyze three different P2P distributed protocols. The analytical tool is compared with results coming from simulation. Outcomes confirm that the approach can be employed to dynamically tune the peers' attachment rate and maintain the desired topology of the P2P network.