Sublimating surfaces are out of equilibrium. It has been proposed that sublimation can be compensated by an impinging atomic ux to obtain equilibrium. This work concerns the eect of such an impinging ux on the stability of surfaces in various situations. For this purpose we combine Kinetic Monte Carlo Simulations with analytical developements based on the Burton-Cabrera-Frank (BCF) classical theory. We show that a perfect compensation of the sublimation is possible for vicinal surfaces but not when 2D islands are present on a surface. We thus study the eect of an impinging ux on the dynamic of a 2D island on a surface. We show that the 2D island area generally varies with time t as −t α. In absence of any impinging ux the value of the exponent α enables to identify the main mechanism at work (diusion limited or attachment-detachment limited). On the contrary, in presence of an impinging ux the value of the exponent α is not enough to identify the main mechanism limiting the area change.