We present APRE, a replication method for structureless Peer-to-Peer overlays. The goal of our method is to achieve real-time replication of even the most sparsely located content relative to demand. APRE adaptively expands or contracts the replica set of an object in order to improve the sharing process and achieve a low load distribution among the providers. To achieve that, it utilizes search knowledge to identify possible replication targets inside query-intensive areas of the overlay. We present detailed simulation results where APRE exhibits both efficiency and robustness relative to the number of requesters and the respective request rates. The scheme proves particularly useful in the event of flash crowds, managing to quickly adapt to sudden surges in load.