In this work, the contribution of the pairwise H(2) addition to the overall reaction mechanism was studied under the systematic variation of both the Pd particle size and the properties of the catalyst support using the hydrogenation of propene and propyne over supported Pd catalysts as representative examples. For Pd supported on alumina, silica and zirconia, only propene formed upon hydrogenation of propyne with para-H(2) exhibits hyperpolarization. In contrast, propane formed in hydrogenation of propyne or propene is not hyperpolarized. This demonstrates the existence of different routes of H(2) addition to double and triple bonds on supported Pd catalysts. The unique ability of Pd/TiO(2) catalysts to add H(2) in a pairwise manner not only to the triple but also to the double bond is demonstrated. This finding indicates that the Pd-support interaction is of primary importance in determining not only the magnitude of the hyperpolarization of the NMR lines of the reaction products but even the involvement of the pairwise H(2) addition and hence the mechanism of heterogeneous hydrogenation. The comparative analysis of the selectivities toward pairwise H(2) addition suggested the existence of different surface active sites responsible for all three reaction routes: the direct total hydrogenation of propyne into propane, its selective hydrogenation into propene, and hydrogenation of propene into propane. A reaction scheme which accounts for the formation of the observed hyperpolarized and non-polarized reaction products in propyne and propene hydrogenation with para-H(2) over supported Pd catalysts is suggested. For the first time, application of the PHIP technique allowed us to demonstrate that hydrogenation of propene does not take place in the presence of propyne on supported Pd catalysts.