We challenge the conventional view that the majority of Mg II/Lyman li
mit absorbers are extended halos of galaxies comprised of ''clouds'' w
ith near-unity covering factor. The gaseous disks of spiral galaxies a
re known to extend to large radii and likely contribute a significant
cross section for absorption. We perform a Monte Carlo survey of QSO f
ields in which the model galaxies have Mg II absorbing ''clouds'' in a
spherical halo or in a randomly oriented disk. For both geometries, m
odels that recover the observed properties of Mg II absorbers have onl
y a 70%-80% covering factor. Therefore, regardless of absorber geometr
y, a survey of randomly selected QSO fields should yield a nonnegligib
le number of nonabsorbing galaxies at small impact parameters. Very fe
w have been observed (Steidel). However, selection effects are importa
nt, and once the observational procedures are applied to our model fie
lds, we find that this result is expected. Since both spherical halo a
nd 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.