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A distinct trend has emerged that the Internet is used to transport data on a more and more massive scale. Capacity shortage in the backbone networks has become a genuine possibility, which will be more serious with fiber-based access. The problem addressed in this paper is how to conduct massive content distribution efficiently in the future network environment, where the capacity limitation can equally be at the core or the edge. We propose a novel technique as a main content transport mechanism to achieve efficient network resource utilization. The technique uses multiple trees for distributing different file pieces, which at the heart is a version of swarming. In this paper, we formulate an optimization problem for determining an optimal set of distribution trees as well as the rate of distribution on each tree under bandwidth limitation at arbitrary places in the network. The optimal solution can be found by a distributed algorithm. The results of the paper not only provide stand-alone solutions to the massive content distribution problem, but should also help the understanding of existing distribution techniques such as BitTorrent or FastReplica.