We consider the influence of realistic island diffusion rates to homoepitaxial growth on metallic surfaces using a recently developed rate equation model which describes growth in the submonolayer regime with hyperthermal deposition. To this end, we incorporate realistic size and temperature-dependent island diffusion coefficients for the case of homoepitaxial growth on Cu(100) and Cu(111) surfaces. We demonstrate that the generic features of growth remain unaffected by the details of island diffusion, thus validating the generic scenario of high density of small islands found experimentally and theoretically for large detachment rates. However, the details of the morphological transition and scaling of the mean island size are strongly influenced by the size dependence of island diffusion. This is reflected in the scaling exponent of the mean island size, which depends on both temperature and the surface geometry. (c) 2005 Elsevier B.V. All rights reserved.