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The objective of several techniques including fluid limits and mean field approximations is to analyze a stochastic complex system (e.g. Markovian) studying a simplified model (deterministic, represented by ordinary differential equations (ODEs)). In this paper, we explore models proposed for the analysis of BitTorrent P2P systems and we provide the arguments to justify the passage from the stochastic process, under adequate scaling, to a fluid approximation driven by an ODE. We also make the link between the stationary regime of the stochastic models and the fixed points of the associated ODEs. Finally, we analyze the asymptotic distribution of the scaled process.