As the use of IP multicast sessions becomes widespread, the potential benefits derived from currently unavailable topological information on multicast distribution trees may become increasingly critical. We propose a framework for discovering the topology of shared multicast trees based on a novel fan-out decrement mechanism analogous to time-to-live (TTL) decrementing in IP. We propose an algorithm for topology discovery based on the matrix of path/fan-out distances among a set of E session members-the algorithm's computational complexity is O(|E|/sup 2/). We exhibit sufficient conditions for topology discovery based on a reduced distance matrix, and propose a practical protocol to acquire this information requiring the exchange of 2|E| multicast messages of size O(|E|). Finally, we show how the same approach permits nodes to discover the multicast distribution tree associated with members within their fan-out/TTL scoped neighborhoods. This permits one to reduce the computational costs while making the communication costs proportional to the size of neighborhoods.