  We present a measurement of the HI column density distribution function,
f(N), at the present epoch for column densities log N > 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
appears 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) in the local Universe by using 21cm synthesis observations of a
complete sample of spiral galaxies. We show that f(N) for damped Ly alpha
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 log N > 21^-2.
