We consider critical percolation on Galton-Watson trees and prove quenched analogues of classical theorems of critical branching processes. We show that the probability critical percolation reaches depth n is asymptotic to a tree-dependent constant times n. Similarly, conditioned on critical percolation reaching depth n, the number of vertices at depth n in the critical percolation cluster almost surely converges in distribution to an exponential random variable with mean depending only on the… Expand