and its scatter is sensitive to the underlying selection function, and can be understood as an interplay between (i) drawing from the full galaxy population at every redshift; (ii) the existence of a mass-metallicity relation at every redshift [@Ledoux2005; @Moller2013; @Christensen2014]; and (iii) a metallicity gradient within each galaxy reflecting the gradual build-up of metals in the interstellar medium (ISM) and CGM by stellar feedback and supernovae explosions. Although metallicity measurements in sub-DLAs rely on ionisation corrections [see e.g., @Zafar2017], these systems are believed to be more chemically enriched than DLAs on average -in particular at low redshifts [@Peroux2006; @Kulkarni2007; @Meiring2009; @Som2013; @Som2015], and there are indications that sub-DLAs arise in more massive galaxies [@Kulkarni2010], which may be caused by selection biases [@Dessauges2009].

The existence of a statistically significant anti-correlation between $\log _{10} [\mathrm{N}_\mathrm{\ion{H}{i}}~(\mathrm{cm}^{-2})]$ and projected separation based on photometric redshift identifications of hosts was demonstrated by [@Rao2011]. This is consistent with spectroscopically confirmed systems which indicate that absorbers are distributed over different impact parameters; sub-DLAs showing larger and more scattered impact parameters than DLAs [@Moller1998; @Christensen2007; @Monier2009; @Fynbo2010; @Fynbo2011; @Meiring2011; @Krogager2012; @Noterdaeme2012; @Peroux2012; @Fynbo2013; @Krogager2013; @Rahmani2016]. This distribution is observed in $z \gtrsim 2$ simulations, and is attributed to 