We investigate the spreading of ⁴He droplets on alkali-metal surfaces at zero temperature, within the frame of finite range density-functional theory. The equilibrium configurations of several ⁴He_N clusters and their asymptotic trend with increasing particle number N, which can be traced to the wetting behavior of the quantum fluid, are examined for nanoscopic droplets. We discuss the size effects inferring the the asymptotic properties of large droplets correspond to those of the prewetting film.