We present here ^{13}C and ^{133}Cs NMR spin lattice relaxation T_{1} data in the A15 and fcc-Cs_{3}C_{60} phases for increasing hydrostatic pressure through the transition at p_{c} from a Mott insulator to a superconductor. We evidence that for p>> p_{c} the (T_{1}T)^{-1} data above T_{c} display metallic like Korringa constant values which match quantitatively previous data taken on other A_{3}C_{60} compounds. However below the pressure for which T_{c} goes through a maximum, (T_{1}T)^{-1} is markedly increased with respect to the Korringa values expected in a simple BCS scenario. This points out the importance of electronic correlations near the Mott transition. For p > p_{c} singular T dependences of (T_{1}T)^{-1} are detected for T >> T_{c}. It will be shown that they can be ascribed to a large variation with temperature of the Mott transition pressure p_{c} towards a liquid-gas like critical point, as found at high T for usual Mott transitions.
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