Potential energy curves of the Auger state Ar+(2p(-1))-Ar, the different one- and two-site dicationic states Ar2 ++ (with energies in the range of 32-77 eV), and the lowest two-site tricationic states Ar++ - Ar+ (with energies in the range of 64-76 eV) computed using elaborated ab initio methods are reported. The accessible relaxation channels of the electronic states of Ar++ - Ar populated by Auger decay are studied. In particular, we study in detail the interatomic Coulombic decay following the population of one-site satellite states of Ar++(3s(-1)3p(-1))-Ar recently observed experimentally. Other relaxation pathways of Ar++ - Ar, including radiative charge transfer, nuclear dynamics through curve crossing, and intra-atomic decay processes are also investigated.