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We report on the formation of ordered and size homogeneous InAs quantum dot (QD) arrays on patterned GaAs(001) substrates. A material depletion region is observed around the patterned area while a long-range homogeneous distribution of QDs is found inside the patterned area. A sample with less InAs deposition shows a gradient in the material distribution over the patterned area. Based on these observations we propose a simple model to describe the QD formation in the patterned area. The QD shape evolution is also investigated and discussed.