  We derive a general formula for renormalized entanglement entropy in even
dimensional CFTs holographically dual to Einstein gravity in one dimension
higher. In order to renormalize, we adapt the Kounterterm method to
asymptotically locally AdS manifolds with conical singularities. On the gravity
side, the computation considers extrinsic counterterms and the use of the
replica trick a la Lewkowycz-Maldacena. The boundary counterterm B_d is shown
to satisfy a key property, in direct analogy to the Euler density: when
evaluated on a conically singular manifold, it decomposes into a regular part
plus a codimension-2 version of itself located at the conical singularity. The
renormalized entropy thus obtained is shown to correspond to the universal part
of the holographic entanglement entropy, which for spherical entangling
surfaces is proportional to the central charge a that is the subject of the
a-theorem. We also review and elucidate various aspects of the Kounterterm
approach, including in particular its full compatibility with the Dirichlet
condition for the metric at the conformal boundary, that is of standard use in
holography.
