  Counterterm actions are constructed along the ADM formalism. It is shown that
the counterterm action can be intrinsically written in terms of intrinsic
boundary geometry. Using the expression of counterterm action, we obtain a
general form of the counterterm action available for any $d$-dimensional
spherical boundary. In the description, we also derive {\it arbitrary}
dimensional holographic conformal anomaly. It is also shown that counterterm
actions for AF spaces can be obtained from the AdS description just as taking
the limit of $\ell \to \infty$. An asymptotically flat spacetime with
non-spherical boundary is speculated. In the example, additional counterterms
to eliminate (leading) divergent terms due to deviation of boundary from round
sphere are imagined by observing (4-dimensional) holographic anomaly
proportional to $\Box R$. Argument of the deceptive-like anomaly is given by
comparing with the holographic description of 5-dimensional Kerr-AdS spacetime.

High Energy Physics - Theory;General Relativity and Quantum Cosmology