Left panel: estimate of the concentration of molecular gas in the central regions of the galaxies of GATOS and NUGA samples derived from the ratio of the average H₂ surface densities measured at two spatial scales: r ≤ 50 pc () and r ≤ 200 pc (); these scales are characteristic of the nuclear and circumnuclear regions, respectively. The ratio (index-I) is represented as a function of the AGN luminosities measured in the 2–10 keV band in log units; symbols are color-coded as a function of the Eddington ratios for the sample galaxies: NUGA (square markers) and GATOS (circle markers). Right panel: same as left panels but replacing by the average H₂ surface densities measured inside the torus (or polar) regions identified in Sect. 4.2 for GATOS sources (index-II). For NUGA galaxies we adopted the torus sizes derived by Combes et al. (2019). Errorbars account for the range of uncertainties on the molecular gas mass ratio estimates due to the assumed conversion factors, discussed in Sect. 8.1 (∼±0.2 dex), and on the AGN luminosities (∼±0.15 dex).