  We consider f(R) gravity theories in the presence of a scalar field minimally
coupled to gravity with a self-interacting potential. When the scalar field
backreacts to the metric we find at large distances scalarized
Schwarzschild-AdS and Schwarzschild-AdS-like black hole solutions. At small
distances due to strong curvature effects and the scalar dynamis we find a rich
structure of scalarized black hole solutions. When the scalar field is
conformally coupled to gravity we also find scalarized black hole solutions at
small distances.
