  We use simulations of the formation and evolution of the galaxy population in
the Local Universe to address the issue of whether the standard theoretical
model succeeds in producing empty regions as large and as dark as the observed
nearby ones. We follow the formation of galaxies in an LCDM universe and work
with mock catalogues which can resolve the morphology of LMC sized galaxies,
and the luminosity of objects 6 times fainter. We look for a void signature in
sets of virialized haloes selected by mass, as well as in mock galaxy samples
selected according to observationally relevant quantities, like luminosity,
colour, or morphology. We find several void regions with diameter 10 Mpc/h in
the simulation where gravity seems to have swept away even the smallest haloes
we were able to track. We probe the environment density of the various
populations and compute luminosity functions for galaxies residing in
underdense, mean density and overdense regions. We also use nearest neighbour
statistics to check possible void populations, taking $L_{*}$ spirals as
reference neighbours. Down to our resolution limits, we find that all types of
galaxies avoid the same regions, and that no class appears to populate the
voids defined by the bright galaxies.
