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"Peer-to-Peer (P2P) networks are fast emerging as a viable and cost effective alternative for content delivery on the Internet. While the fast growth of P2P networks has generated substantial interest, rigorous theoretical studies of the diffusion process in P2P networks have been largely absent. Our paper represents one of the first studies of the diffusion process in P2P networks and of the impact of network structure and upload rebates - rewards for users who share their resources - on the speed of diffusion. Starting with an analogy between P2P diffusion and epidemic diffusion, we develop a stochastic diffusion model for flat P2P networks. We find that product diffusion in P2P networks is likely to follow classic S-shaped processes. Next, we develop a deterministic approximation that is computationally efficient and expand our study to account for generation of multiple requests and forwarding of requests. Finally, we model hierarchical topologies in P2P networks. We find that offering rebates to users who share content with others is effective in speeding product diffusion. We also find that network structure exerts a dominant influence on diffusion and determines whether and how other parameters like rebates, fraction of nodes that are unselfish, etc. influence the rate of diffusion. Our results suggest that a hierarchical architecture with a few groups degrades system performance in terms of diffusion rate only slightly. Simulation results suggest that our models yield good predictions. The analytical models presented in this paper serve as a starting point for rigorous modeling and study of content diffusion in P2P networks."