By showing that there is a topologically free boundary action, we prove that the outer automorphism groups of the topological full groups of the Cuntz?Krieger groupoids are C*-simple, meaning that their reduced C*-algebras are simple (this is an extreme case of non-amenability). These groups generalise the outer automorphism groups of the Higman?Thomson groups, so our result applies, in particular to, Out(V_n), where V_n is a Higman?Thompson group. This is joint work with Xin Li and Takuya Takeishi.