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We consider conditioned Galton-Watson trees and show asymptotic normality ofadditive functionals that are defined by toll functions that are not too large.This includes, as a special case, asymptotic normality of the number of fringesubtrees isomorphic to any given tree, and joint asymptotic normality forseveral such subtree counts. Another example is the number of protected nodes.The offspring distribution defining the random tree is assumed to haveexpectation 1 and finite variance; no further moment condition is assumed.

Asymptotic normality of fringe subtrees and additive functionals in conditioned Galton--Watson trees