Crystal growth on a semi-infinite surface is considered. The remaining semi-infinite part of the plane is covered with a mask on which no crystal growth can occur. The mass-transfer coefficient ks which measures the rate at which the surface reaction proceeds, is considered to be finite. Together with the diffusion coefficient D this parameter defines a characteristic time t and length ¿. A solution valid for large t is derived. It is shown that crystal-growth conditions change markedly within a neighbourhood of the mask edge whose length is of the order of ¿. Outside this region crystal growth is almost fully diffusion-controlled. Within the region surface control exerts its influence, but the grown layer is much thicker there than elsewhere. As long as the grown layer is much thinner than ¿, growth at the mask edge is kinetically controlled.