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Media distribution through application-layer overlay networks has received considerable attention recently, owing to its flexibility and readily deployable nature. On-demand streaming with asynchronous requests and, in general, with VCR-like interactions nevertheless remains a challenging task in overlay networks. In this paper, we introduce the dynamic skip list (DSL), a novel randomized and distributed structure that inherently accommodates dynamic and asynchronous clients. We establish the theoretical foundations of the DSL and demonstrate a practical DSL-based streaming overlay. In this overlay, the costs for typical operations, including join, leave, fast-forward, rewind, and random seek, are all sublinear to the client population. The model also seamlessly integrates a smart data scheduling algorithm using linear network coding, yielding fast and robust downloading from multiple suppliers. Our simulation results show that the DSL-based overlay is highly scalable. It delivers reasonably smooth playback with diverse client interactivities while keeping the computation and bandwidth overheads low.