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