We study the formation of nanoholes and quantum rings in GaAs and AlGaAs surfaces by local droplet etching with Inx Ga1-x. The rings are crystallized from droplet material and surround the nanohole openings. In particular, the influence of the In content x on density, diameter, and depth of the nanoholes is investigated. Our data establish an exponential dependence of these quantities on x, which is quantitatively reproduced by a model that considers different surface diffusion energy barriers for Ga and In. By etching with pure In, hole densities as low as 5× 106 cm-2 have been achieved. In addition, for low In content incompletely removed initial droplets are visible on the surface. These droplets are not visible on samples with x