Soft deposition of Co nanoclusters on a Cu(001) substrate is studied by constant‐temperature molecular‐dynamics simulations. A different epitaxial behaviour of the clusters has been found as a function of the number of atoms. At room temperature, Co clusters grow epitaxially below two hundred atoms. Some of these clusters show stacking faults. Larger clusters do not achieve epitaxy. In these clusters, influence of the substrate is small and only affects the zone nearest to the interface, which becomes epitaxial. By increasing temperature and deposition energy, it is possible to enlarge the parts of the cluster grown epitaxially even attaining a complete epitaxy. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)