Damped H I-Ly-α lines for the proximate H₂ systems. The X-shooter data are shown in black, and the profile corresponding to best fit is shown in red. The red shadows represent the conservative range of N(H I), including continuum placement uncertainties. There is residual Ly-α emission in the core of several DLAs. We also mark the expected position of the N Vλλ1238, 1242 doublet in blue. The tick marks represent the range seen in low-ionisation species (i.e. z₅ and z₉₅). It is here detected in all cases but J1259+0309 and J1331+0206.