Galaxy disks are shown to contain a significant population of atomic clouds of 100pc linear size which are self-opaque in the 21cm transition. These objects have HI column densities as high as 10^23 and contribute to a global opacity correction factor of 1.34+/-0.05 that applies to the integrated 21cm emission to obtain a total HI mass estimate. Opacity-corrected images of the nearest external galaxies have been used to form a robust z=0 distribution function of HI, f(N_HI,X,z=0), the probability of encountering a specific HI column density per unit comoving distance. This is contrasted with previously published determinations of f(N_HI,X) at z=1 and 3. A systematic decline of moderate column density (18<log(N_HI)<21) HI is observed that corresponds to a decline in surface area of such gas by a factor of five since z=3. The number of equivalent DLA absorbers (log(N_HI)>20.3) has also declined systematically over this redshift interval by a similar amount, while the cosmological mass density in such systems has declined by only a factor of two to its current, opacity corrected value of Omega_HI^DLA(z=0) = 5.4 +/- 0.9x10^-4. We utilize the tight, but strongly non-linear dependence of 21cm absorption opacity on column density at z=0 to transform our HI images into ones of 21cm absorption opacity. These images are used to calculate distribution and pathlength functions of integrated 21cm opacity. The incidence of deep 21cm absorption systems is predicted to show very little evolution with redshift, while that of faint absorbers should decline by a factor of five between z=3 and the present. We explicitly consider the effects of HI absorption against background sources that are extended relative to the 100pc intervening absorber size scale. Future surveys of 21cm absorption will require very high angular resolution, of about 15mas, for their unambiguous interpretation. (Abridged.)
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