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Over the past few years, peer-to-peer (P2P) systems have become very popular for constructing overlay networks of many nodes (peers) that allow users geographically distributed to share data and resources. One non-trivial question is how to distribute the data in a fair and fully decentralized manner among the peers. This is important because it can improve resource usage, minimize network latencies and reduce the volume of unnecessary traffic incurred in large-scale P2P systems. In this paper we present a technique for fair resource allocation in unstructured peer-to-peer systems. Our technique uses the fairness index of a distribution as a measure of fairness and shows how to optimize the fairness of the distribution using only local decisions. Load balancing is achieved by replicating documents across multiple nodes in the system. Our experimental results demonstrate that our technique is scalable, has low overhead and achieves good load balance even under skewed demand.