  We present results from a spectroscopic and imaging survey of galaxies in the
fields of quasars from the HST Quasar Absorption Line Key Project. The aim of
this survey is to identify galaxies within 3.5' from the quasar sightline, to a
limiting r-band magnitude mr = 22.5. The data are then compared to the HST
homogeneous sample of Lyman-alpha-only absorbers in order to put constraints on
the nature of these absorbers, and in particular on their relation to galaxies.
The analysis of our sample combined with those of previous studies shows that:
1) the redshift agreements of the Ly-alpha absorber-galaxy associations cannot
be due to chance coincidence; 2) there is no clear anti-correlation between the
Ly-alpha rest-frame equivalent width and the impact parameter for the whole
sample. Our results suggest that most Ly-alpha absorbers are not gaseous clouds
that belong in a strict sense to galaxies, as is the case for MgII absorbers.
The fraction of associations to the total number of galaxies at impact
parameter < D as a function of D drops from 1 to 0.65 at D = 200 H50 kpc and
flattens at larger values of D (> 300 H50 kpc), which leads to Ly-alpha
galactic halos sizes about three times larger than the inner MgII halo region;
3) there is no correlation between the galaxy luminosity and the impact
parameter. This again suggests that a significant Ly-alpha clouds do not belong
to individual galaxies, but instead are distributed in the local large-scale
structure. 4) the HWHM=120 km/s of the relative velocity distribution of the
Ly-alpha absorber-galaxy associations is consistent with either galaxy rotation
velocities or the local velocity dispersion in large-scale structures.
