Critical mass ratios (above which mass transfer is stable) for 1 M_⊙ and 4 M_⊙ donor stars as a function of donor radius, under different criteria for stable mass transfer (see Sect. 3). The solid black line shows the critical mass ratios resulting from our quasi-adiabatic criterion, with the grey shading indicating the parameter space where mass transfer would be unstable. The red lines show the critical mass ratios resulting from the dynamical evolution criterion with A_dyn = 0.01, 0.05, 0.25, as indicated to the right end of the lines. The solid orange line shows the critical mass ratios resulting from the OLOF-based criterion, and the solid blue line and hatching show where the Darwin instability could be encountered (see Sect. 5.2). The solid horizontal grey line shows where M_a/M_d = 1, and the dashed vertical grey lines show the end of the HG phase (panel a and left line in panel b) and the tip of the RGB (panel b).