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 starbursty hosts. Overall, reservoirs of 10⁷ ≲ M_H2 ≲ 10¹⁰ M_⊙ are seen at z < 0.3, and 10¹⁰ ≲ M_H2 ≲ 10¹² M_⊙ at z> 1. Taking into account the completeness correction of the sample, we created the corresponding H₂ 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.

Reduced datacubes are also available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (ftp://130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/668/A67