Molecular glasses can grow crystals much faster at the free surface than in the interior. A property of this process is the creation of depressed grooves Of depletion zones around the crystals on the initially flat amorphous surface. With scanning electron microscopy and atomic force microscopy, we Studied this phenomenon in indomethacin; which crystallizes in two polymorphs (alpha and gamma) of different morphologies,. observed depletion zones are well reproduced by the known coefficients of surface diffusion and the velocities of crystal growth. At the slow growing flank: of needle like alpha IMC crystals; depletion zones widen and,deepen over time according to the expected kinetics for surface diffusion responding to a crystallization flux. Before fast advancing growth fronts, depletion zones have less time to develop; their steady-state dimensions agree with the same model revised for a moving phase boundary. These results support the view that surface diffusion enables fast surface,crystal growth on molecular glasses. Our finding helps understand crystal growth in thin films in which the formation of deep depletion zones can cause dewetting and alter growth kinetics.