  We study higher dimensional gravitational collapse to topological black holes
in two steps. Firstly, we construct some (n+2)-dimensional collapsing
space-times, which include generalised Lemaitre-Tolman-Bondi-like solutions,
and we prove that these can be matched to static $\Lambda$-vacuum exterior
space-times. We then investigate the global properties of the matched solutions
which, besides black holes, may include the existence of naked singularities
and wormholes. Secondly, we consider as interiors classes of 5-dimensional
collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to
radiating exteriors given by the Bizon-Chmaj-Schmidt metric. In some cases, the
data at the boundary for the exterior can be chosen to be close to the data for
the Schwarzschild solution.
