Methods of producing high uniformity in thin film transistor devices fabricated on laterally crystallized thin films are described. A thin film transistor (TFT) includes a channel area disposed in a crystalline substrate, which has grain boundaries that are approximately parallel with each other and are spaced apart with approximately equal spacings. The shape of the channel area includes a non-equiangular polygon that has two opposing side edges that are oriented substantially perpendicular to the grain boundaries. The polygon further has an upper edge and a lower edge. At least a portion of each of the upper and lower edges is oriented at a tilt angle with respect to the grain boundaries. The tilt angles are selected such that the number of grain boundaries covered by the polygon is independent of the location of the channel area within the crystalline substrate.