We study kinetic factors governing the diffusion and desorption of covalently grafted phenyl and dichlorocarbene radicals on graphene and carbon nanotubes. Our ab initio calculations of reaction rates show that isolated phenyls can easily desorb and diffuse at room temperature. On the contrary, paired phenyls are expected to remain grafted to the surface up to a few hundred degrees Celsius. In the case of dichlorocarbene, no clustering is observed; at room temperature, the isolated radicals remain covalently attached to small-diameter nanotubes but desorb easily from graphene. Our results on the thermal behavior of side moieties on graphitic surfaces could be used to optimize the tradeoff between reactivity and conductance of nanotubes in the process of covalent functionalization.