The interaction of a curved polycyclic aromatic hydrocarbon (PAH), corannulene (C20H10) with H-atoms leading to the formation of highly superhydrogenated species was studied. In particular, we determined the H-atom addition sequence to a monolayer of corannulene deposited on a graphite surface in order to understand the effect of curvature on the interaction of PAHs with H-atoms. We also investigated why superhydrogenated corannulene species with a certain number of additional H-atoms are more stable than the others. A combination of thermal desorption mass spectrometry measurements and density functional theory calculations was used to reveal and understand the presence of the most stable configurations in the superhydrogenation sequence of corannulene. Specifically, the experiments demonstrate the presence of stable configurations of superhydrogenated corannulene at specific hydrogenation levels of 2, 6, 8, 10, 12, 14, 16, 17 and 18 extra H-atoms. Density functional theory calculations of binding energies and barrier heights explain why some of these configurations are particularly stable and provide new insights into the superhydrogenation of curved PAH molecules under interstellar conditions.