Integrated 21-cm optical depth corrected for partial coverage assuming f_c = f_VLBA vs. linear size (in pc) at the absorber redshift for the sample S2. Systems towards the quasars with no “core” identifications are plotted as squares. 21-cm detections are shown as filled symbols and 21-cm non-detections are represented by open symbols. The point for the system towards B1629+120 with LS = 7.2 kpc is not plotted to keep LS-axis short.