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We generalize recent results of Haas and Miermont to obtain scaling limits ofMarkov branching trees whose size is specified by the number of nodes whoseout-degree lies in a given set. We then show that this implies that the scalinglimit of finite variance Galton-Watson trees condition on the number of nodeswhose out-degree lies in a given set is the Brownian continuum random tree. Thekey to this is a generalization of the classical Otter-Dwass formula.

Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given set