  Additive tree functionals represent the cost of many divide-and-conquer
algorithms. We derive the limiting distribution of the additive functionals
induced by toll functions of the form (a) n^\alpha when \alpha > 0 and (b) log
n (the so-called shape functional) on uniformly distributed binary search
trees, sometimes called Catalan trees. The Gaussian law obtained in the latter
case complements the central limit theorem for the shape functional under the
random permutation model. Our results give rise to an apparently new family of
distributions containing the Airy distribution (\alpha = 1) and the normal
distribution [case (b), and case (a) as $\alpha \downarrow 0$]. The main
theoretical tools employed are recent results relating asymptotics of the
generating functions of sequences to those of their Hadamard product, and the
method of moments.
