We demonstrate that the formation of GaAs quantum wires on self-limiting AlGaAs grown on V grooves occurs via a transient increase of the growth rates in a set of different nanofacets. Upon growth of sufficiently thick layers on AlGaAs, the GaAs surface reaches a self-limiting profile as well, through an equalization of the relative growth rates on these facets. Atomic force microscopy studies show that the step density in the facets along the groove evolves with GaAs thickness in the same way as the facets extension, thus suggesting a role of the step distribution in the establishment of the self-limiting profiles. The self-limiting GaAs groove profile is much broader than the AlGaAs one at corresponding growth temperatures; however, it can be sharpened down to a radius of curvature of 5 nm for T = 550°C. Under these conditions, GaAs was successfully used as a barrier material for growing vertical arrays of self-ordered InGaAs wires.