  We use a sample of 64 nearby (D=7-45 Mpc) disk galaxies including 45 AGN and
19 non-AGN, that have high spatial resolution multiline CO observations
obtained with the ALMA and/or PdBI arrays to study the distribution of cold
molecular gas in their circumunuclear disks (CND). We analyze whether the
concentration of cold molecular gas changes as a function of the X-ray
luminosity in the 2-10 keV range ($L_{\rm X}$). We also study the concentration
of the hot molecular gas using NIR data obtained for the H2 1-0S(1) line. We
find a turnover in the distribution of the cold molecular gas concentration as
a function of $L_{\rm X}$ with a breakpoint which divides the sample into two
branches: the AGN build-up branch ($L_{\rm X}\leq10^{41.5\pm0.3}$erg/s) and the
AGN feedback branch ($L_{\rm X}\geq10^{41.5\pm0.3}$erg/s) . Lower luminosity
AGN and non-AGN of the AGN build-up branch show high cold molecular gas
concentrations and centrally peaked radial profiles on nuclear ($r\leq50$~pc)
scales. Higher luminosity AGN of the AGN feedback branch, show a sharp decrease
in the concentration of molecular gas and flat or inverted radial profiles. The
cold molecular gas concentration index ($CCI$), defined as the ratio of surface
densities at $r\leq50$~pc and $r\leq200$~pc , namely $CCI \equiv$~log$_{\rm
10}(\Sigma^{\rm gas}_{\rm 50}/\Sigma^{\rm gas}_{\rm 200}$), spans a factor ~4-5
between the galaxies lying at the high end of the AGN build-up branch and the
galaxies of the AGN feedback branch. The concentration and radial distributions
of the hot molecular gas in our sample follow less extreme trends as a function
of the X-ray luminosity. These observations confirm, on a three times larger
sample, previous evidence found by the GATOS survey that the imprint of AGN
feedback on the CND-scale distribution of molecular gas is more extreme in
higher luminosity Seyfert galaxies of the local universe.
