  Using data on the HI column density distribution in the local Universe,
f(N_{HI}), we show how to determine g(N_{H}), the distribution of the total gas
(HI+HII) column density. A simple power law fit to f(N_{HI}) fails due to
bendings in the distributions when N_{HI}<10^{20} cm^{-2} and H is no longer
fully neutral. If an ultraviolet background is responsible for the gas
ionization, and g(N_{H}) is proportional N_{H}^{-alpha}, we find the values of
alpha and of the intensity of the background radiation which are compatible
with the present data. These best fitting values, however, depend upon the
scaling law of the the gas volume densities with N_{H} and cannot be determined
unambiguously. We examine in detail two models: one in which the average gas
volume density decreases steadily with N_H, while in the other it stays
constant at low column densities. The former model leads to a steep power law
fit for g(N_{H}), with alpha of order 3.3 +- 0.4 and requires an ultraviolet
flux larger than what the QSOs alone produce at z=0. For the latter alpha is
1.5 +- 0.1 and a lower ionizing flux is required. The ambiguities about the
modelling and the resulting steep or shallow N_{H} distribution can be resolved
only if new 21-cm observations and QSOs Lyman limit absorbers searches will
provide more data in the HI-HII transition region at low redshifts. Using the
best fit obtained for higher redshift data we outline two possible scenarios
for the evolution of gaseous structures, compatible with the available data at
z=0.
