Title: The Percolation Process on a Tree Where Infinite Clusters are Frozen. Author: David J. Aldous Abstract: Modify the usual percolation process on the infinite binary tree by forbidding infinite clusters to grow further. The ultimate configuration will consist of both infinite and finite clusters. We give a rigorous construction of a version of this process and show that one can do explicit calculations of various quantities, for instance the law of the time (if any) that the cluster containing a fixed edge becomes infinite. Surprisingly, the distribution of the shape of a cluster which becomes infinite at time $t>1/2$ does not depend on $t$; it is always distributed as the incipient infinite percolation cluster on the tree. Similarly, a typical finite cluster at each time $t>1/2$ has the distribution of a critical percolation cluster. This elaborates an observation of Stockmayer (1942).