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We report on the morphological evolution of InGaN/GaN light-emitting diodes (LEDs) grown on nominally on-axis and intentionally misoriented free-standing m-plane GaN substrates. Large variations in p-n junction depth (±175nm) were observed for LEDs grown on nominally on-axis substrates, while negligible variations in junction depth (±20 nm) were observed for LEDs grown on intentionally misoriented substrates. The surfaces of LEDs grown on the nominally on-axis substrates were characterized by the presence of a high density of pyramidal hillocks [Hirai etal, Appl. Phys. Lett. 91, 191906 (2007)], while the surfaces of the LEDs grown on the intentionally misoriented substrates were relatively smooth and free of pyramidal hillocks. Detailed measurements indicated that the variations in junction depth observed for LEDs grown on nominally on-axis substrates were related to an evolution in the shape of individual pyramidal hillocks during the growth of the LEDs. These results indicate that growing LEDs on intentionally misoriented substrates is an effective way to eliminate the pyramidal hillocks and variations in junction depth associated with growth on nominally on-axis substrates.