  We consider counterterms for odd dimensional holographic CFTs. These
counterterms are derived by demanding cut-off independence of the CFT partition
function on $S^d$ and $S^1 \times S^{d-1}$. The same choice of counterterms
leads to a cut-off independent Schwarzschild black hole entropy. When treated
as independent actions, these counterterm actions resemble critical theories of
gravity, i.e., higher curvature gravity theories where the additional massive
spin-2 modes become massless. Equivalently, in the context of AdS/CFT, these
are theories where at least one of the central charges associated with the
trace anomaly vanishes. Connections between these theories and logarithmic CFTs
are discussed. For a specific choice of parameters, the theories arising from
counterterms are non-dynamical and resemble a DBI generalization of gravity.
For even dimensional CFTs, analogous counterterms cancel log-independent
cut-off dependence.
