Growth of Mg-doped GaN on trench-patterned GaN films consists of competing lateral and vertical growth fronts that result in regions with different electronic properties. Under typical growth conditions, lateral growth from the trench sidewall occurs at a faster rate than vertical growth from the trench base. When the trench width is sufficiently narrow, the growth fronts from opposite sidewalls coalesce and lead to eventual planarization of the top surface. Secondary electron imaging and cathodoluminescence mapping are used to correlate the morphology and the optical properties of regions resulting from lateral and vertical growth. For our growth conditions, the lateral-to-vertical growth rate ratio is found to be about 2.