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An Internet flash crowd (also known as hot spots) is a phenomenon that results from a sudden, unpredicted increase in an on-line object's popularity. Currently, there is no efficient means within the Internet to deliver Web objects scalably under hot spot conditions to all clients that desire the object. We present peer-to-peer (P2P) randomized overlays to obviate flash-crowd symptoms (PROOFS), a simple, lightweight, P2P approach that uses randomized overlay construction and randomized, scoped searches to locate and deliver objects efficiently under heavy demand to all users that desire them. We evaluate PROOFS' robustness in environments in which clients join and leave the P2P network, as well as in environments in which clients are not always fully cooperative. Through a mix of simulation and prototype experimentation in the Internet, we show that randomized approaches like PROOFS should effectively relieve flash crowd symptoms in dynamic, limited-participation environments.