GaAs nanostructures are promising candidates for use in future nanoelectronics and quantum photonics. However, technology of their controllable fabrication with precisely predefined size, shape and surface density still requires further improvement. In this paper, we reveal a possibility to reduce a size of gallium droplets using exposure to the arsenic flux of ultra-low values. The control of size and shape of droplets is implemented independently of their surface density that enables formation of low-density arrays of small-sized quantum dots. Based on droplet arrays with trimodal size distribution, we demonstrate that droplets with larger sizes are less influenced by the low arsenic flux whereas smaller droplets may reduce in volume or decay completely resulting in the formation of nanoholes. The technique under consideration can be used for the fabrication of single quantum dot devices with specified  characteristics.