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Additive tree functionals allow to represent the cost of manydivide-and-conquer algorithms. We give an invariance principle for such treefunctionals for the Catalan model (random tree uniformly distributed among thefull binary ordered trees with given number of internal nodes) and for simplygenerated trees (including random tree uniformly distributed among the orderedtrees with given number of nodes). In the Catalan model, this relies on thenatural embedding of binary trees into the Brownian excursion and then onelementary second moment computations. We recover results first given by Filland Kapur (2004) and then by Fill and Janson (2009). In the simply generatedcase, this relies on the convergence of conditioned Galton-Watson towardsstable L\'evy trees. We recover results first given by Janson (2003 and 2016)in the quadratic case and give a generalization to the stable case.

Cost functionals for large (uniform and simply generated) random trees