We present density functional theory (DFT) calculations of the electronic and magnetic properties of fluorine adatoms on a single side of a graphene monolayer. By extrapolating the results, the binding energy of a single fluorine adatom on graphene in the dilute limit is calculated. Our results confirm that the finite-size error in the binding energy scales inversely with the cube of the linear size of the simulation cell. We establish relationships between stability and C–F bond nature, diffusion of fluorine adatoms and total magnetization in different configurations of adatoms. For single-side fluorination, sp 2.33 is the maximum p-content re-hybridization found in the C–F bond. We show that semilocal DFT cannot predict correctly the magnetic properties of fluorinated graphene and a higher level theory, such as DFT+U is needed. The results indicate a tendency of graphene to reduce the imbalance between adsorption on the two sublattices, and therefore total magnetization, through low-energy-barrier pathways on a time scale of ~10 ps at room temperature. The thermodynamically favored arrangements are those with the smallest total magnetization. Indeed, the electronic structure is intimately related to the magnetic properties and changes from semi-metallic to p-type half-metallic or semiconducting features, depending on the adatoms arrangement.