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.
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