The adsorption of water on the TiO2(110) surface has become the model process in efforts to understand metal oxide-aqueous solution interfaces. Considerable progress has been made in understanding low-coverage situations where first-principle calculations have been employed to good effect. However, current theory is less well developed for coverage above one monolayer. Here we present results of calculations on the adsorption process in forming the second water layer, that is, the adsorption of water on the fully hydrated surface. We show that there are many competitive adsorption sites owing to the numerous hydrogen-bonding possibilities. The presence of the second layer water molecules facilitates proton transfer among the adsorbates within chainlike configurations, and we present some illustration of these processes. We show how the adsorption energetics computed here along with recent calculations on defective surface and low-coverage adsorption may be used to provide a satisfactory interpretation of the temperature programmed desorption data for this system. Finally, we compute the vibrational spectrum for H and compare with the high-resolution electron-energy-loss spectroscopy measurements. (C) 2003 American Institute of Physics.