  We challenge the conventional view that the majority of MgII/Lyman limit
absorbers are extended halos of galaxies comprised of ``clouds'' with
near-unity covering factor. The gaseous disks of spiral galaxies are known to
extend to large radii and likely contribute a significant cross-section for
absorption. We perform a Monte-Carlo survey of QSO fields in which the model
galaxies have MgII absorbing ``clouds'' in a spherical halo or in a randomly
oriented disk. For both geometries, models that recover the observed properties
of MgII absorbers have only a 70-80% covering factor. Therefore, regardless of
absorber geometry, a survey of randomly selected QSO fields should yield a
non-negligible number of non-absorbing galaxies at small impact parameters.
Very few have been observed (Steidel (1995)). However, selection effects are
important, and once the observational procedures are applied to our model
fields we find that this result is expected. Since both spherical halo and disk
models can be made consistent with survey results, we present tests for
discerning the geometric distribution of absorbing gas from Hubble Space
Telescope images and high resolution spectra.
