  We have used STIS aboard HST to search for Lyman-alpha (Lya) absorption lines
in the outer regions of eight nearby galaxies using background QSOs and AGN as
probes. Lya lines are detected within a few hundred km/s of the systemic
velocity of the galaxy in all cases. We conclude that a background
line-of-sight which passes within 26-200 h-1 kpc of a foreground galaxy is
likely to intercept low column density neutral hydrogen with log N(HI) >~ 13.0.
The ubiquity of detections implies a covering factor of ~ 100% for low N(HI)
gas around galaxies within 200 h-1 kpc. We discuss the difficulty in trying to
associate individual absorption components with the selected galaxies and their
neighbors, but show that by degrading our STIS data to lower resolutions, we
are able to reproduce the anti-correlation of Lya equivalent width and impact
parameter found at higher redshift. We also show that the equivalent width and
column density of Lya complexes (when individual components are summed over ~
1000 km/s) correlate well with a simple estimate of the volume density of
galaxies brighter than M(B) = -17.5 at the same redshift as a Lya complex. We
do not reject the hypothesis that the selected galaxies are directly
responsible for the observed Lya lines, but our analysis indicates that
absorption by clumpy intragroup gas is an equally likely explanation. (Abriged)
