H/r-profile (top), temperature (middle) and surface density profile (bottom) of discs with different Ṁ rates. The profile is taken when the discs have reached their radially constant Ṁ rate. The black dotted lines represent power-law fits to guide the eyes. The grey area in the temperature plot marks the temperature range where the opacity profile changes due to the melting of ice grains (see Fig. 1). Please note that we cut the displayed disc at 30 AU to enhance the details in the inner parts of the disc.