We present a comprehensive study of the nucleation kinetic of Cu on Ni~100! using variable-temperature scanning tunneling microscopy. The analysis of the saturation island density as a function of substrate temperature and deposition rate reveals that the smallest stable island abruptly changes from a dimer to a tetramer. From the Arrhenius plot, the migration barrier Em5~0.3560.02! eV, as well as the dimer bond energy Eb5~0.4660.19! eV, has been deduced. For low ratios between the migration constant D and flux R (D/R,10 4 ), nucleation and island growth take place not only during, but also after deposition. In this postnucleation regime, the final island density and island size distribution are no more determined by the competition between flux and monomer migration, but solely by the monomer concentration present immediately after deposition. Therefore, the island density becomes independent of substrate temperature and flux, and the scaled island size distribution closely resembles that of statistic growth ~adatom smallest stable island!. The experimental results are compared with simulations using rate equations. @S0163-1829~96!10948-6# Quantitative understanding of the nucleation and growth of heteroepitaxial films is challenging both from a fundamental and a technological point of view, as it establishes how the film morphology is related to the growth conditions. The fundamental processes during submonolayer growth involve adatom diffusion, nucleation, aggregation, and coalescence, all being controlled by the external parameters of deposition rate and substrate temperature. Proceeding with the deposition on a defect-free substrate, the adatoms can migrate, meet further adatoms, and form nuclei. These nuclei either dissociate ~subcritical size ,i! or, for the critical ones ~size i!, grow to stable islands upon the incorporation of one extra atom. These islands then continue to grow and at a coverage between 0.1 and 0.2 monolayers ~ML!, the island density usually saturates, just before coalescence of the islands sets in. The dependence of the saturation island density on substrate temperature and flux can be used to extract microscopic parameters such as activation barriers for surface migration and dimer dissociation by means of mean-field