We have measured the column density distribution function , f ( N _ { HI } ) , at z = 0 using 21-cm Hi emission from galaxies selected from a blind Hi survey . f ( N _ { HI } ) is found to be smaller and flatter at z = 0 than indicated by high-redshift measurements of Damped Lyman- \alpha ( DLA ) systems , consistent with the predictions of hierarchical galaxy formation . The derived DLA number density per unit redshift , dN _ { DLA } / dz = 0.058 , is in moderate agreement with values calculated from low-redshift QSO absorption line studies . We use two different methods to determine the types of galaxies which contribute most to the DLA cross-section : comparing the power law slope of f ( N _ { HI } ) to theoretical predictions and analysing contributions to dN _ { DLA } / dz . We find that comparison of the power law slope can not rule out spiral discs as the dominant galaxy type responsible for DLA systems . Analysis of dN _ { DLA } / dz however , is much more discriminating . We find that galaxies with \log \mbox { $M _ { HI } $ } < 9.0 make up 34 % of dN _ { DLA } / dz ; Irregular and Magellanic types contribute 25 % ; galaxies with surface brightness , \overline { \mu } _ { 25 } > 24 mag arcsec ^ { -2 } account for 22 % and sub- L _ { * } galaxies contribute 45 % to dN _ { DLA } / dz . We conclude that a large range of galaxy types give rise to DLA systems , not just large spiral galaxies as previously speculated .