Self-assembled nanoholes are drilled into (001) AlGaAs surfaces during molecular beam epitaxy (MBE) using local droplet etching (LDE) with Al droplets. It is known that this process requires a small amount of background arsenic for droplet material removal. The present work demonstrates that the As background can be supplied by both a small As flux to the surface as well as by the topmost As layer in an As-terminated surface reconstruction acting as a reservoir. We study the temperature-dependent evaporation of the As topmost layer with in situ electron diffraction and determine an activation energy of 2.49 eV. After thermal removal of the As topmost layer droplet etching is studied under well-defined As supply. We observe with decreasing As flux four regimes: planar growth, uniform nanoholes, non-uniform holes, and droplet conservation. The influence of the As supply is discussed quantitatively on the basis of a kinetic rate model.