Consider a rooted tree with leaf-set and with all nonleaf vertices having out-degree 2, at least. A rooted tree with leaf-set is induced by in if is the lowest common ancestor subtree for , with all its degree-2 vertices suppressed. A “maximum agreement subtree” (MAST) for a pair of two trees and is a tree with a largest leaf-set such that is induced by both in and . Bryant, McKenzie, and Steel [BioConsensus, AMS, Providence, RI, 2003, pp. 55–65] and Bernstein et al. [SIAM J. Discrete Math., 29 (2015), pp. 2065–2074] proved, among other results, that for and being two independent copies of a random binary (uniform or Yule–Harding distributed) tree , the likely magnitude order of is . We prove this bound for a wide class of random rooted trees: is a terminal tree of a branching, Galton–Watson, process with an ordered-offspring distribution of mean 1, conditioned on “total number of leaves is .”