  To evaluate the role of radio activity in galaxy evolution, we designed a
large archival CO survey of radio galaxies (RGs) to determine their molecular
gas masses at different epochs. We used a sample of 120 RGs representative of
the NVSS 1.4 GHz survey, when flux limited at 0.4 Jy. Of those, 66 galaxies
belonged to the ALMA Radio-source Catalogue (ARC) of calibrators and had
spectral window tunings around CO (1-0), (2-1), (3-2), or (4-3). We reduced
their ALMA data, determined their H2 mass contents, and combined the results
with similar results for the remaining 54 galaxies from the literature. We
found that, while at all epochs the majority of RGs have undetectable
reservoirs, there is a rapid increase in the H2 mass content of the CO-detected
RGs with z. At 1<z<2.5, one-fourth of the RGs have at least as much molecular
gas as simulations would indicate for a typical halo mass of that epoch. These
galaxies plausibly have ``normal'' or even starburst hosts. Taking into account
the completeness correction of the sample, we created the corresponding H$_2$
mass functions at 0.005<z<0.3 and 1<z<2.5. The local mass function reveals that
the number density of low-z RGs with detectable molecular gas reservoirs is
only a little lower (a factor of ~4) than that of pure (or little star-forming)
type 1 and 2 AGN in simulations. At 1<z<2.5, there is a significant decrease in
the number density of high-z RGs due to the rarity of bright radio galaxies. An
estimate for the missing faint RGs would, nonetheless, bring populations close
again. Finally, we find that the volume density of molecular gas locked up in
the brightest 1/5000-1/7000 RGs is similar in the examined $z$ bins. This
result likely indicates that the inflow rate on one hand and the star-formation
depletion rate plus the jet-driven expulsion rate on the other hand counteract
each other in the most luminous RGs of each epoch.
