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In this paper we obtain the scaling law for the mean broadcast time of a file in a P2P network with an initial population of N nodes. In the model, at Poisson rate lambda a node initiates a contact with another node chosen uniformly at random. This contact is said to be successful if the contacted node possesses the file, in which case the initiator downloads the file and can later upload it to other nodes. In a network with altruistic nodes (i.e., nodes do not leave the network) we show that the mean broadcast time is O(log(N)). In a network with free-riding nodes, our main result shows that a O(log(N)) mean broadcast time can be achieved if nodes remain connected to the network for the duration of at least one more contact after downloading the file, otherwise a significantly worse O(N) time is required to broadcast the file.