Transistor structures including a non-planar body that has an active portion comprising a semiconductor material of a first height that is variable, and an inactive portion comprising an oxide of the semiconductor material of a second variable height, complementary to the first height. Gate electrodes and source/drain terminals may be coupled through a transistor channel having any width that varies according to the first height. Oxidation of a semiconductor material may be selectively catalyzed to convert a desired portion of a non-planar body into the oxide of the semiconductor material. Oxidation may be enhanced through the application of a catalyst, such as one comprising metal and oxygen, for example.