  Smooth spacetimes possessing a (global) one-parameter group of isometries and
an associated Killing horizon in Einstein's theory of gravity are investigated.
No assumption concerning the asymptotic structure is made, thereby, the
selected spacetimes may be considered as generic distorted stationary black
holes. First, spacetimes of arbitrary dimension, $n\geq 3$, with matter
satisfying the dominant energy condition and allowing non-zero cosmological
constant are investigated. In this part complete characterisation of the
topology of the event horizon of ``distorted'' black holes is given. It is
shown that the topology of the event horizon of ``distorted'' black holes is
allowed to possess a much larger variety than that of the isolated black hole
configurations. In the second part, 4-dimensional (non-degenerate) electrovac
distorted black hole spacetimes are considered. It is shown that the spacetime
geometry and the electromagnetic field are uniquely determined in the black
hole region once the geometry of the bifurcation surface and one of the
electromagnetic potentials are specified there. Conditions guaranteeing the
same type of determinacy, in a neighbourhood of the event horizon, on the {\it
domain of outer communication} side are also investigated. In particular, they
are shown to be satisfied in the analytic case.
