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We present DFT+U based electronic structure calculations in a p(3 x 3) slab supercell, for low coverages of atomically dispersed Rh interacting with the CeO2(111) surface, comparing Rh as an adatom, and as a dopant substituted into the surface layer. We find that, energetically, a Rh atom approaching a ceria(111) surface with both sparse O and Ce vacancies present strongly prefers to heal the Ce vacancies, but next it prefers to adsorb on a stoichiometric region rather than healing an O vacancy. In the adatom system, Rh is oxidized by electron transfer to a 4f orbital on one Ce ion in the surface layer, which is then nominally converted from Ce4+ -> Ce3+ (i.e. Rh adatoms are single donors). We show that there are a number of different local minima, with Ce3+ localization at 1st, 2nd or 3rd nearest neighbour Ce sites. The second neighbour is the most stable, but all are close in energy. In the Rh-doped system (Rh replaces Ce), Rh is oxidized by charge transfer to neighbouring O atoms, and Rh doping leads to deep acceptor and donor states. Rh is not stable in the O sublattice. Moreover, based on vacancy formation energies, we find that oxygen vacancy formation is strongly enhanced in the vicinity of Rh dopants, but slightly suppressed in the vicinity of Rh adatoms.