  The Damped Lyman-alpha systems (DLAs), seen in absorption in the spectrum of
quasars, are believed to contain a large fraction of the neutral gas in the
Universe. Paradoxically, these systems are more difficult to observe at
z_abs<1.7, since they are rare and their HI feature then falls in UV spectra.
Rao & Turnshek (2000) pioneered a method based on MgII-selected DLAs, that is
absorbers discovered thanks to our knowledge of their MgII feature in optical
spectra. We use new observations undertaken at the TNG as well as a careful
literature & archival search to build samples of low redshift absorbers
classified according to the technique used for their discovery. We successfully
recover N(HI) and equivalent widths of FeII 2600, MgII 2796, MgII 2803 and MgII
2852 for a sample of 36 absorbers, 21 of which are MgII-selected. We find that
the MgII-selected sample contains a marginally larger fraction of absorbers
with log N(HI)>21.0 than seen otherwise at low redshift. If confirmed, this
property will in turn affect estimates of Omega_HI which is dominated by the
highest HI column densities. We find that log N(HI) does not correlate
significantly with metal equivalent widths. Similarly, we find no evidence that
gravitational lensing, the fraction of associated systems or redshift evolution
affect the absorber samples in a different way. We conclude that the hint of
discrepancies in N(HI) distributions most likely arises from small number
statistics. Therefore, further observations are required to better clarify the
impact of this discrepancy on estimates of Omega_HI at low redshift.
