Generalised gradient approximation (PBE) and hybrid (PBE0) density functional theory (DFT) within the periodic electrostatic embedded cluster method have been used to study AnO2 bulk and surfaces (An = U, Np, Pu). The electronic structure has been investigated by examining the projected density of states (PDOS). While PBE incorrectly predicts these systems to be metallic, PBE0 finds them to be insulators, with the composition of the valence and conduction levels agreeing well with experiment. Molecular and dissociative water adsorption on the (111) and (110) surfaces of UO2 and PuO2 has been investigated, with that on the (110) surface being stronger than on the (111). Similar energies are found for molecular and dissociative adsorption on the (111) surfaces, while on the (110) there is a clear preference for dissociative adsorption. Adsorption energies and geometries on the (111) surface of UO2 are in good agreement with recent periodic DFT studies using the GGA+U approach, and our data for dissociative adsorption on the (110) surface of PuO2 match experiment rather well, especially when dispersion corrections are included.