The emission area of GaN light-emitting diodes can be patterned by etch-free current aperturing methods which exploit the thin and highly resistive nature of the p-doped layer in these devices. Here, the fundamental underlying electrical and optical aspects of high-resolution current aperturing are investigated theoretically. The most critical parameter for the possible resolution is the thickness d of the p-GaN layer, but the interplay of p-GaN resistivity and electrical junction characteristics is also important. A spatial resolution of 1.59d can in principle be achieved, corresponding to about 300 nm in typical epitaxial structures. Furthermore, the emission from such a small emitter will spread by about 600 nm while propagating through the p-GaN. Both values can be reduced by reducing d.