In this paper it is shown that the number of induced subgraphs (the set of edges is induced by the set of nodes) of trees of size satisfy a central limit theorem and that multivariate asymptotic expansions can be obtained. In the case of planted plane trees, -ary trees, and non-planar rooted labelled trees, explicit formulae can be given. Furthermore, the average size of the largest component of induced subgraphs in trees of size is evaluated asymptotically.
