Complexes of Li, Na and Mg with graphene, silicene, phosphorene nanoflakes (NFs) and their 2D allotropies have been studied at dispersion corrected TPSS/def-TZVP level of theory. The energy partition analysis of the complexes revealed that for most of the complexes exchange and correlation energies represent dominant contributions to the binding with strong charge transfer from metal atom to a NF. The exceptions are Mg complexes of graphene and phosphorene NFs where binding is due to dispersion and correlation terms. This difference is also reflected in large Mg-NF distances suggesting weak intermolecular interactions in these complexes. The calculated activation energies for metal hopping are easily achievable at room temperatures for carbon and silicon allotropies. However, they are significantly higher for phosphorus allotropies reaching almost 18 kcal/mol. There is a reasonably good correlation between the activation energies for hopping and binding energies for graphene, silicene and phosphorene NFs. Such correlation is not observed however for graphene, silicene and phosphorene 2D allotropies