Present routes to produce magnetic organic-based materials adopt a common strategy: the use of magnetic species (atoms, polyradicals, etc.) as building blocks. We explore an alternative approach which consists of selective hydrogenation of Polycyclic Aromatic Hydrocarbons. Self-Consistent-Field (SCF) (Hartree-Fock and DFT) and multi-configurational (CISD and MCSCF) calculations on coronene and corannulene, both hexa-hydrogenated, show that the formation of stable high spin species is possible. The spin of the ground states is discussed in terms of the Hund rule and Lieb's theorem for bipartite lattices (alternant hydrocarbons in this case). This proposal opens a new door to magnetism in the organic world.