Gaseous halos of nine nearby galaxies ( with redshifts cz < 6000 km s ^ { -1 } ) were probed at large galactocentric radii using background quasars observed with HST GHRS and STIS . The projected quasar-galaxy separations range from 55 to 387 h ^ { -1 } _ { 75 } kpc . Ly \alpha absorption lines were successfully detected in the spectra of five quasars , at impact parameters of up to \sim 170 h ^ { -1 } _ { 75 } kpc from the center of the nearby galaxy , and in each case at wavelengths consistent with the galaxy ’ s redshift . Our observations include the lowest redshift Ly \alpha lines detected to date . HI velocity fields were obtained at the VLA for three of the galaxies in our sample ( and in one case was available from the literature ) , to derive their rotation curves . When comparing the inner rotation curves of the galaxies with the velocity at large radius provided by the Ly \alpha line it is apparent that it is very difficult to explain the observed Ly \alpha velocity as due to gas in an extended rotating disk . In most cases one would need to invoke large warps in the outer gas disks and also thick gas disks in order to reconcile the observed velocities with the predicted ones . Indeed , in one case the Ly \alpha line velocity indicates in fact counter-rotation with respect to the inner disk rotation . In light of these results we conclude that in a typical galaxy there is no longer detectable atomic gas corotating in an extended disk at radii > 35 \alpha ^ { -1 } , where \alpha ^ { -1 } is the stellar disk exponential scale-length . The cosmic web is the most likely origin for the detected Ly \alpha lines . Our observations confirm the Bowen et al . ( 2002 ) correlation of equivalent widths with the local volume density of galaxies around the sightline , and the observed equivalent widths of the lines are consistent with expectations of the cosmic web .