In recent years, overlay networks have proven a popular way of disseminating potentially large files from a single server S to a potentially large group of N end users via the Internet. A number of algorithms and protocols have been suggested, implemented and studied. In particular, much attention has been given to peer-to-peer (P2P) systems such as BitTorrent, Slurpie, SplitStream, Bullet and Avalanche. The key idea is that the file is divided into M parts of equal size and that a given user may download any one of these -- or, for Avalanche, linear combinations of these -- either from the server or from a peer who has previously downloaded it. However, performance analysis of P2P systems for file dissemination has typically been limited to comparing one system relative to another and typically been realized by means of simulations and measurements. We give the minimal time to fully disseminate the file of M parts from a server to N end users in a centralized scenario. In the scheduling literature this completion time is referred to as makespan. We thereby provide a lower bound which can be used as a performance benchmark for any P2P file dissemination system. We also investigate the part of the loss in efficiency that is due to the lack of centralized control in practice. Using simulation as well as direct computation, we show that even a simple and natural randomized strategy disseminates the file in an expected time that grows with N in a similar manner to the minimal time achieved with a centralized controller. This suggests that the performance of necessarily decentralized P2P file dissemination systems should still be close to our performance bound.