AbstractWe present a measurement of the HI column density distribution function f(N_hi) at the present epoch for column densities > 10²⁰ cm⁻². These high column densities compare to those measured in damped Lyα lines seen in absorption against background quasars. Although observationally rare, it appears that the bulk of the neutral gas in the Universe is associated with these damped Lyα systems. In order to obtain a good anchor point at z = 0 we determine f(N_hi) in the local Universe by using 21 cm synthesis observations of a complete sample of spiral galaxies. We show that f(N_hi) for damped Lyα systems has changed significantly from high z to the present and that change is greatest for the highest column densities. The measurements indicate that low surface brightness galaxies make a minor contribution to the cross section for HI, especially for N_HI > 10²¹ cm⁻².