  We study the perturbative behaviour of topological black holes in the
presence of a cosmological constant and a scalar field coupled to the
Gauss-Bonnet term. We calculate both analytically and numerically the
quasi-normal modes of scalar perturbations in the extended
scalar-tensor-Gauss-Bonnet gravity. In the case of small black holes we find a
phase transition of the topological black hole to a hairy configuration.
