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To improve rendered video quality and serve more receivers, peer-to-peer (P2P) video-on-demand streaming systems usually deploy seed servers. These servers complement the limited upload capacity offered by peers. In this paper, we are interested in optimally managing the capacity of seed servers, especially when scalable video streams are served to peers. Scalable video streams are encoded in multiple layers to support heterogeneous receivers. We show that the problem of optimally allocating the seeding capacity to serve scalable streams to peers is NP-complete. We then propose an approximation algorithm to solve it. Using the proposed allocation algorithm, we develop an analytical model to study the performance of P2P video-on-demand streaming systems and to manage their resources. The analysis also provides an upper bound on the maximum number of peers that can be admitted to the system in flash crowd scenarios. We validate our analysis by comparing its results to those obtained from simulations. Our analytical model can be used by administrators of P2P streaming systems to estimate the performance and video quality rendered to users under various network, peer, and video characteristics.