We study the optical emission of single GaAs quantum dots (QDs). The QDs are fabricated by filling of nanoholes in AlGaAs and AlAs which are generated in a self-assembled fashion by local droplet etching with Al droplets. Using suitable process parameters, we create either uniform QDs in partially filled deep holes or QDs with very broad size distribution in completely filled shallow holes. Micro photoluminescence measurements of single QDs of both types establish sharp excitonic peaks. We measure a fine-structure splitting in the range of 22–40μeV and no dependence on QD size. Furthermore, we find a decrease in exciton–biexciton splitting with increasing QD size.