Experiments have shown that the efficiency of nanoporous carbons to store hydrogen becomes enhanced by doping the material with metallic nanoparticles. In particular, doping with palladium has been used with success. The hypothesis to justify the enhancement has been that the Pd nanoparticles dissociate the hydrogen molecules and then the hydrogen atoms spill over the carbon substrate, where the hydrogen is retained. To test this hypothesis we have performed ab initio molecular dynamics simulations of the deposition of molecular hydrogen on Pd nanoparticles (Pd6 and Pd13) supported on graphene, which is a good model for the wall of a carbon nanopore. Three channels have been identified in the simulations: bouncing off the molecule, molecular adsorption, and dissociation of the molecule in two H atoms. The relative percentage of those channels is sensitive to the size of the Pd particle. Dissociation occurs more frequently on Pd13 and it generally takes place on the lateral regions of the Pd particles. However, in our simulations, we have not found a single case of H atoms or H2 molecules spilling over the carbon substrate. We have also tested the situation when several H atoms are preadsorbed on the Pd6 and Pd13 particles and found that not a single dissociation event occurs on these H-saturated nanoparticles. These results lead us to cast strong doubts on the validity of the spillover mechanism for explaining the enhancement of hydrogen adsorption on porous carbons doped with transition metal nanoparticles. M.B.-R., J.I.J. and M.A. acknowledge support by Basque Departamento de Educación, Universidades e Investigación, the University of the Basque Country UPV/EHU (Grant No. IT-756-13) and the Spanish Ministerio de Economía y Competitividad (Grant No. FIS2013-48286-C2-2-P). J.A.A. and M.J.L. acknowledge support by MINECO (Grant No. MAT2014-54378-R) and Junta de Castilla y León (Grant No. VA050U14). The authors thankfully acknowledge the computer resources provided by the DIPC computing center. Peer reviewed