The reactivity of H(2) on several gold clusters is studied using density functional theory with generalized gradient approximation methods, as model systems designed to study the main effects determining their catalytic properties under controlled conditions. Border effects are studied in finite linear gold chains of increasing size and compared with the corresponding periodic systems. In these linear chains, the reaction can proceed with no barrier along the minimum energy path, presenting a deep chemisorption well of approximately 1.4 eV. The mechanism presents an important dependence on the initial attacking site of the chain. Linear Au(4) chains joined to model-nanocontacts, formed by 2 or 3 gold atoms, in a planar triangle or in a pyramid, respectively, are also studied. The reaction barriers found in these two cases are approximately 0.24 and 0.16 eV, respectively, corresponding to H(2) attacking the more coordinated edge atom of the linear chain. The study is extended to planar clusters with coordinations IV and VI, for which higher H(2) dissociation barriers are found. However, when the planar gold clusters are folded, and the Au-Au distances elongated, the reactivity increases considerably. This is not due to a change of coordination, but to a larger flexibility of the gold orbitals to form bonds with hydrogen atoms, when the planar sd-hybridization is broken. Finally, it is concluded that the major factor determining the reactivity of gold clusters is not strictly the coordination of gold atoms but their binding structure and some border effects.