Maximal penetration length l_max (red) and length of the layer where the bulk of the plumes penetrate l_bulk (blue curves), in units of the pressure scale height at the convective boundary, as a function of the luminosity of the model. The solid curves and circles are the values derived from the use of f_k and the dashed curves and triangles corresponds to the values derived from f_δT. The dotted curves show power laws L^0.23 and L^0.3 as guide for the eyes.