  Generic black holes in vacuum-de Sitter / Anti-de Sitter spacetimes are
studied in quasi-local framework, where the relevant properties are captured in
the intrinsic geometry of the null surface (the horizon). Imposing the
quasi-local notion of stationarity (null symmetry of the metric up to second
order at the horizon only) we perform the complete classification of all the so
called special Petrov types of these surfaces defined by the properties
(structure of principal null direction) of the Weyl tensor at the surface. The
only possible types are: II, D and O. In particular all the geometries of type
O are identified. The condition distinguishing type D horizons, taking the form
of a second order differential equation on certain complex invariant
constructed from the Gaussian curvature and the rotation scalar, is shown to be
an integrability condition for the so called near horizon geometry equation.
The emergence of the near horizon geometry in this context is equivalent to the
hyper-suface orthogonality of both double principal null directions. We further
formulate a no-hair theorem for the Petrov type D axisymmetric null surfaces of
topologically spherical sections, showing that the space of solutions is
uniquely parametrized by the horizon area and angular momentum.
