  Application of concepts like black hole and event horizon in cosmological
context are not trivial, as has been shown in the last decade. We introduce
special solutions of the LTB family representing collapsing over-dense regions
extending to an expanding closed, open, or flat FRW model asymptotically. We
study the dynamics of the collapsing region, and its density profile. The
question of the strength of the central singularity and its nakedness, as well
as the existence of an apparent horizon and an event horizon is dealt with in
detail. Differences to the Schwarzschild black hole are addressed.
