One of the key questions in dimensioning a hybrid P2P content distribution system is that of the required infrastructure support in terms of server bandwidth. In this paper, we develop and propose simple mathematical models for analyzing and dimensioning hybrid peer-to-peer content distribution networks. We first use a deterministic fluid model to capture the essential peer and server dynamics within a single swarm, and subsequently derive a stochastic fluid model to capture the dynamics in the case of multiple swarms, i.e., concurrent swarms of a number of content objects. Based on the models, we derive solutions for estimating the server capacity required to support a single swarm as well as a number of concurrent file swarms at a given level of service quality. Numerical results demonstrate how a hybrid P2P approach can yield substantial performance gains and capacity savings compared to a pure client/server system, with churn rate and upload bandwidth being critical factors. Compared to a pure peer-to-peer scenario, the hybrid approach can dramatically boost the performance and improve reliability.