We address the problem of content replication in large distributed content delivery networks, composed of a data center assisted by many small servers with limited capabilities and located at the edge of the network. We aim at optimizing the placement of contents on the servers to offload the data center as much as possible. We model the sub-system constituted by the small servers as a loss network, each loss corresponding to a request to the data center. Based on large system / storage behavior, we obtain an asymptotic formula for the optimal replication of contents and propose adaptive schemes to attain it by reacting to losses, as well as faster algorithms which can react before losses occur. We show through simulations that our adaptive schemes outperform significantly standard replication strategies both in terms of loss rates and adaptation speed.