—The paper addresses the problem of massive content distribution in the network where multiple sessions coexist. In the traditional approaches, the sessions form separate overlay networks and operate independently from each other. In this case, some sessions may suffer from insufficient resources (e.g., aggregate upload bandwidth) even though other sessions have excessive resources. To cope with this problem, we consider the universal swarming approach, which allows multiple sessions cooperate with each other by forming a shared overlay network. We formulate the problem of finding the optimal resource allocation to maximize the sum of the session utilities under the network capacity constraints. The solution turns out to be optimal sharing of multiple minimum-cost multicast trees. We first present a subgradient algorithm and prove that, although the algorithm uses a single multicast tree per session at each iteration and hence does not converge in the conventional sense, it conver...