The evolution of the morphology of small clusters grown on a complex surface containing a regular network of defects is investigated in the case of Co on Au(1 1 1). On the basis of molecular dynamics calculations the existence of a critical size for the transition from mono- to bi-layer islands is inferred. Rather than strain effects, the final bilayer morphology of the deposit is conditionned by the demixtion tendency in the bulk (Co, An) alloy, favoring Co-Co bonds against heteroatomic ones, and surface tension effects both going towards a prefered three-dimensional growth. (C) 2003 Elsevier B.V. All rights reserved.