Comparison of two prescriptions for the maximum (i.e. disc limited) gas accretion rate, the one presented in this work (labelled ‘Bondi rate’) with that of Mordasini et al. (2012c) (labelled ‘Flow rate’). These are two different simulations (one for each prescription) whose initial conditions represent the second outermost planet in Fig. 4. Top panel: maximum value that can be supplied by the gas disc (labelled ‘Max.’) and effective accretion rates (labelled ‘Eff.’), which is given by intrinsic cooling in the initial attached phase and the maximum rate in the detached phase. Bottom panel: corresponding enveloppe mass (i.e. total gas accreted).