The growth kinetics of vertical III−V nanowires (NWs) were clarified long ago. The increasing aspect ratio of NWs results in an increase in the surface area, which, in turn, enhances the material collection. The group III adatom diffusion from the NW sidewalls to the top sustains a superlinear growth regime. In this work, we report on the growth of different GaAs nanostructures by selective area MOVPE on GaAs (111)B substrates. We show that the opening dimensions and geometry qualitatively alter the morphology and height evolution of the structures. We compare the time evolution of vertical GaAs NWs stemming from circular holes and horizontal GaAs nanomembranes (NMs) growing from one-dimensional (1D) rectangular slits on the same substrate. While NW heights grow exponentially with time, NMs surprisingly exhibit sublinear kinetics. The absence of visible atomic steps on the top facets of both NWs and NMs suggests layer-by-layer growth in the mononuclear mode. We interpret these observations within a self-consistent growth model, which links the diffusion flux of Ga adatoms to the position-and shape-dependent nucleation rate on top of NWs and NMs. Specifically, the island nucleation rate is lower on top of the NMs than that on the NWs, resulting in the total diffusion flux being directed from the top facet to the sidewalls. This gives a sublinear height evolution for the NMs. These results open innovative perspectives for shape engineering of III−V nanostructures and new avenues for the design of optoelectronics and photonic devices.