Results for a run with the full quasar background from Fig. 2 (C1; thick solid line) and runs with 2 times (C1b; thick dashed line) and 4 times (C1c; thick dotted line) the fiducial quasar background, all at ﹩z=3﹩. Top: H I column density frequency distribution ﹩f( N,X) ﹩. The two thin lines are the SDSS DLA survey data as in Fig. 4. Bottom: Line density ﹩l_{\mathrm{DLA}\,}( X) ﹩ of DLAs with the Si II velocity width higher than ﹩v_{\mathrm{Si}\,\,{}^{{\rm{\small II}}}}﹩ vs. ﹩v_{\mathrm{Si}\,\,{}^{{\rm{\small II}}}}﹩. The thin dotted and thin horizontal lines show the observed kinematic distribution as in Fig. 5.