The energetics of monomer, dimer, and triangular trimer adatom islands on the (111) surface of fcc transition metals of the same chemical species is calculated in the tight-binding scheme as a function of the d band filling. Both the adatom and their nearest neighbor substrate atoms are allowed to relax. We investigate all possible atomic configurations of the system arising from the existence of (a) two types of adsorption sites: normal (fcc) and fault (hcp) sites, and (b) both types of borders that may exist for triangles of adatoms: A, having (001), (010), and (100) facets and B, having (111\ifmmode\bar\else\textasciimacron\fi{}), (11\ifmmode\bar\else\textasciimacron\fi{}1), and (1\ifmmode\bar\else\textasciimacron\fi{}11) facets. It is found that there is an inversion of relative stability from fault to normal sites when the d band filling is larger than 8.2d electrons per atom for monomers, 7.85 for dimers, 7.5 for trimers of type A, and 7.6 for trimers of type B. There is also an inversion of stability for trimers from type B to type A when the d band filling is larger than 7.95. All these results are in very good agreement with experiments on Ir for which the d band filling is \ensuremath{\simeq}7.5--7.6: monomers and dimers prefer to stick at fault sites while trimers settle at both sites. Furthermore, triangles of type B are energetically more favored than triangles of type A. The case of other transition metals is also discussed. \textcopyright{} 1996 The American Physical Society.