  We consider some general consequences of adding pure gravitational
Chern-Simons term to manifestly diff-covariant theories of gravity. Extending
the result of a previous paper we enlarge the class of metrics for which the
inclusion of a gCS term in the action does not affect solutions and
corresponding physical quantities. In the case in which such solutions describe
black holes (of general horizon topology) we show that the black hole entropy
is also unchanged. We arrive at these conclusions by proving three general
theorems and studying their consequences. One of the theorems states that the
contribution of the gravitational Chern-Simons to the black hole entropy is
invariant under local rescaling of the metric.
