Abstract: Parallelism in the download process of large files is an efficient mechanism for distributed systems. In such systems, some peers (clients) exploit the power of parallelism to download blocks of data stored in a distributed way over some other peers (servers). Determining response times in parallel downloading with capacity constraints on both the client downloads and server uploads necessitates understanding the instantaneous shares of the bandwidths of each client/server is devoted to each data transfer flow. In this report, we explore the practical relevance of the hypothesis that flows share the network bandwidth according to the max-min fairness paradigm. We have implemented into a flow-level simulator a version of the algorithm which calculates such a bandwidth allocation, which we have called the ``progressive-filling flow-level algorithm''. We have programmed a similar model over NS2 and compared the empirical distributions resulting from both simulations. Our results indicate that flow-level predictions are very accurate in symmetric networks and good in asymmetric networks. Therefore, PFFLA would be extremely useful to build flow-level simulators and, possibly, to perform probabilistic performance calculations in general P2P networks.