  We present a model for the distribution of void sizes and its evolution in
the context of hierarchical scenarios of gravitational structure formation. We
find that at any cosmic epoch the voids have a size distribution which is
well-peaked about a characteristic void size which evolves self-similarly in
time. This is in distinct contrast to the distribution of virialized halo
masses which does not have a small-scale cut-off.
  In our model, the fate of voids is ruled by two processes. The first process
affects those voids which are embedded in larger underdense regions: the
evolution is effectively one in which a larger void is made up by the mergers
of smaller voids, and is analogous to how massive clusters form from the
mergers of less massive progenitors. The second process is unique to voids, and
occurs to voids which happen to be embedded within a larger scale overdensity:
these voids get squeezed out of existence as the overdensity collapses around
them. It is this second process which produces the cut-off at small scales.
  In the excursion set formulation of cluster abundance and evolution, solution
of the cloud-in-cloud problem, i.e., counting as clusters only those objects
which are not embedded in larger clusters, requires study of random walks
crossing one barrier. We show that a similar formulation of void evolution
requires study of a two-barrier problem: one barrier is required to account for
voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void
size distribution is a function of two parameters, one of which reflects the
dynamics of void formation, and the other the formation of collapsed objects.
