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The geometric structure and bonding properties of medium-sized ArnH+ clusters (n = 2-35), in which a proton is wrapped up in a number of Ar atoms, are investigated by applying a diatomics-in-molecules (DIM) model with ab-initio input data generated by means of multi-reference configuration-interaction (MRCI) computations. For the smaller complexes, n = 2-7, cross-checking calculations employing the coupled-cluster approach (CCSD) with the same one-electron atomic basis set as for the input data calculations (aug-cc-pVTZ from Dunning), show good agreement thus justifying the extension of the DIM study to larger n. Local minima of the multi-dimensional potential-energy surfaces (PES) are determined by combining a Monte-Carlo sampling followed, for each generated point, by a steepest-descent optimization procedure. For the electronic ground state of the ArnH+ clusters, the global minimum (corresponding to the most stable structure of the cluster) as well as secondary minima are found and analyzed. The structural and energetic data obtained reveal the building-up regularities for the most stable structures and make it possible to formulate a simple increment scheme. The low-lying excited states are also calculated by the DIM approach; they all turn out to be globally repulsive