  It is by now well established that divergences of the on-shell action for
asymptotically AdS solutions can be cancelled by adding covariant local
boundary counterterms to the action. Here we show that although one can still
renormalise the action for asymptotically $AdS_p \times S^q$ solutions using
local boundary counterterms the counterterm action is not covariant since the
conformal boundary is degenerate. Any given counterterm action is defined with
respect to specific coordinate frame and gauge choices.
