Ab initio density functional theory calculations of hexagonal shaped zigzag edged graphene nanodot molecules, modified by the addition of atomic H to interior and perimeter sites, predict significant changes to the hexagonally sectored spin distribution and chemical bonding of the originals. The redistribution of Kohn-Sham levels at the top of the valence manifold from parent to derivative hint at large changes in the electronic structure. A centrally added H atom creates an occupied level in the middle of the 0.3 eV band gap of the parent molecule and is surrounded by an island of spins. The latter is isolated enough from the perimeter to provide a calibration of the edge spins of the modified parent. Mid-edge addition of a H atom quenches the spin on the edge by drawing a pz-electron into the C-H bond without reducing the spin on the other edges. Addition of H to an apex carbon atom results in a localized spin freed from the double bond that coexists with the parent spin on the same edge. Saturating the apex double bond by adding two H atoms, returns -levels shifted in energy and index and parent-like spin patterns on all edges, intact except for small changes on the edges joined at the apex. Taken in unison these results demonstrate how atomic hydrogen and other groups could be used to engineer the magnetism of graphene nanodots.