Absolute value of the inflow and outflow mass rate as a function of z on the Hill sphere. In the Lm and LmLv cases the mass inflow is larger than the mass outflow except very close to the midplane which appears decreating. Instead, in the N case, the Hill sphere is accreting up to z = 0.2[R_H] and for z > 0.7[R_H]. In all the models, the contribution to the total mass flow in the Hill sphere becomes negligible at z > 0.8[R_H].