We have measured the column density distribution function, f(NH i), at z= 0 using 21-cm H i emission from galaxies selected from a blind H i survey. f(NH i) is found to be smaller and flatter at z= 0 than indicated by high-redshift measurements of damped Lyman α (DLA) systems, consistent with the predictions of hierarchical galaxy formation. The derived DLA number density per unit redshift, dNDLA/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(NH i) to theoretical predictions and analysing contributions to dNDLA/dz. We find that comparison of the power-law slope cannot rule out spiral discs as the dominant galaxy type responsible for DLA systems. Analysis of dNDLA/dz however, is much more discriminating. We find that galaxies with log MH i<9.0 make up 34 per cent of dNDLA/dz; Irregular and Magellanic types contribute 25 per cent; galaxies with surface brightness account for 22 per cent and sub-L* galaxies contribute 45 per cent to dNDLA/dz. We conclude that a large range of galaxy types give rise to DLA systems, not just large spiral galaxies as previously speculated.