perform DFT calculations within the COSMO framework to study the adsorption properties of the CaHPOx (x = 1,...,4) phosphate family, and of the related HPOx acids, on a paradigmatic anatase (001) surface. Of particular interest is CaHPO4, a precursor of hydroxyapatite, which forms during osseointegration of titanium implants. Our results, obtained within the COSMO framework, are based on total energy calculations, and are interpreted in terms of electronegativity differences between the relevant system components. They show that adsorption of HPOx and in particular of HPO4, is highly enhanced by the presence of Ca adatoms on the TiO2 substrate, a result which is in agreement with our previous work on the wettability of anatase surfaces. We also study the adsorption of CaHPOx molecules on TiO2 surfaces, and show that molecular adsorption is strongly favoured for x = 4, while for x = 1, 2 dissociative adsorption of HPOx molecules and Ca adatoms prevails.