Maximum accretion rates of SMSs following the mass-radius relation (Eq. (11)), as a function of their mass, for different ratios in the accretion flow (solid, dashed, and dotted black lines). The limits to hydrostatic equilibrium are shown in grey. The limits of dynamical accretion (Haemmerlé et al. 2019) indicate the maximum rates below which equilibrium is ensured by sound waves, in the core only (solid line) and in the whole star (dashed line); the limit of stability against GR corrections is shown for the non-rotating case (Haemmerlé 2020, 2021a).