Spin polarized density functional theory based calculations within the GGA/PW91 exchange-correlation functional have been carried out to investigate the interaction of Co, Rh, and Ir atoms with the Al-terminated a-Al2O3(0001) surface at 1/3 ML coverage. A periodic supercell approach has been used and two possible spin states of the adsorbed metal atoms have been considered. The predicted adsorption energies follow the order Ir approximate to Co > Rh and it is found that, independently of the spin state and of the relaxation of the oxide substrate, the preferred sites for the adsorption of these metals always involve interaction with surface oxygen atoms. The three transition metal atoms prefer to bind the surface at the 3-fold hollow oxygen sites although for Co the interaction on top of an oxygen adsorption site is practically equivalent. For the three transition metal atoms adsorption on top of the outermost surface aluminum atoms is clearly unfavorable. Explicit consideration of the spin polarization effects is important since Co and It maintain the number of unpaired electrons as in the free atoms whereas a spin quenching is observed for Rh. Metal adsorption is accompanied by some reduction of the substrate leading to a large surface relaxation mainly involving a displacement of the outermost aluminum layer.