We study the zero-temperature phase diagrams of H2 adsorbed on the three structures predicted for graphane (chair, boat and washboard graphane), using a diffusion Monte Carlo technique. Graphane is the hydrogenated version of graphene, in which each carbon atom changes its hybridization to sp3 and forms a covalent bond with a hydrogen atom. Our results show that the ground state of H2 adsorbed on all three types of graphane is a 3 √ ×3 √ solid, similar to the structures found both for H2 and D2 on graphene. When the H2 density increases, the system undergoes a first order phase transition to a triangular incommensurate solid. This change is direct in the case of washboard graphane, but indirect via different commensurate structures in the other cases. The total hydrogen weight percentage on the three graphane types in their ground states is in the range 10 % to 12 %, depending on if one or both graphane surfaces are covered with H2.