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Internet flash crowds (a.k.a. hot spots) are a phenomenon that result from a sudden, unpredicted increase in an on-line object's popularity. Currently, there is no efficient means within the Internet to scalably deliver Web objects under hot spot conditions to all clients that desire the object. We present PROOFS: a simple, lightweight, peer-to-peer (P2P) approach that uses randomized overlay construction and randomized, scoped searches to efficiently locate and deliver objects 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.