HI column density distribution function at z=0: Connection to damped Ly alpha statistics

We present a measurement of the HI column density distribution function f(N -HI) at the present epoch for column densities > 10(20) cm(-2). These high column densities compare to those measured in damped Ly alpha lines seen in absorption against background quasars. Although observationally rare, it a ppears that the bulk of the neutral gas in the Universe is associated with these damped Ly alpha 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 obs ervations of a complete sample of spiral galaxies. We show that f(N-HI) for damped Ly alpha systems has changed significantly from high z to the prese nt and that change is greatest for the highest column densities. The measur ements indicate that low surface brightness galaxies make a minor contribut ion to the cross section for HI, especially for N-HI > 10(21) cm(-2).