S-curve behaviour with respect to the MRI-activated TI and evolution of the inner disc during quiescence. Panel a: S-curves of MREF^*, DUST, and FULL, extracted from the respective quiescent phases (for MREF^* and FULL) compared with the main flares of the accretion events (for all three models) at a radius of 0.2 AU. The arrows along the curves indicate the direction of evolution. The dashed black lines mark the critical values of the surface densities at which the respective upper branches end. The panel also includes the upper branches of the S-curves for the DUST and FULL models at r = 0.08 AU. Panel b: evolution of the surface density during the quiescent phase of FULL. The dashed yellow line is the approximate profile of the hydrostatic structure the disc would adopt if no TI were to occur.