  We study a conformally coupled scalar-tensor theory with a quartic potential
possessing local conformal symmetry up to a boundary term. We show that
requiring the restoration of the full local conformal symmetry fixes the
counterterms that render the on-shell action finite. The building block of the
resulting action is a conformally covariant tensor which is constructed out of
the metric and the scalar field and it has the same conformal weight as the
Weyl tensor. This allows us to obtain the counterterms for the scalar-tensor
sector in a closed form. The finiteness of the conformally complete version of
the action is suggestive on the validity of the Conformal Renormalization
prescription. We extend this theory by adding the Conformal Gravity action and
also the Einstein-AdS action written in McDowell-Mansouri form. Even though the
latter breaks the conformal symmetry, we find that the action is still
renormalized provided a suitable falloff of the scalar field when considering
asymptotically locally anti-de Sitter solutions. Black hole solutions in these
theories are studied, for which the Hawking temperature and the partition
function to first order in the saddle-point approximation are calculated,
providing a concrete example of this renormalization scheme.

High Energy Physics - Theory;General Relativity and Quantum Cosmology