We present a statistical analysis of voids in the 2dF galaxy
redshift survey (2dFGRS). In order to detect the voids, we have
developed two robust algorithms. We define voids as non-overlapping
maximal spheres empty of halos or galaxies with mass or luminosity
above a given one. We search for voids in cosmological $N$-Body
simulations to test the performance of our void finders. We obtain and
analyze the void statistics for several volume-limited samples for the
North Galactic Strip (NGP) and the South Galactic Strip (SGP)
constructed from the 2dFGRS full data release. We find that the
results obtained from the NGP and the SGP are statistically
compatible. From the results of several statistical tests we conclude
that voids are essentially uncorrelated, with at most a mild
anticorrelation and that at the 99.5\% confidence level there is a
dependence of the void number density on redshift. We
develop a technique to correct the distortion caused by the fact that
we use the redshift as the radial coordinate. We calibrate this
technique with mock catalogues and find that the correction might be
of some relevance to carry out accurate inferences from void
statistics. We study the statistics of the galaxies inside nine
nearby voids. We find that galaxies in voids are not randomly distributed:
they form structures like filaments. We also obtain the galaxy number density
profile in voids. This profile follow a similar but steeper trend to that follow by halos
in voids.