The structure of two ordered stoichiometric TiO(2) nanophases supported on Pt(111) and (1x2)-Pt(110) substrates, prepared by reactive evaporation of Ti in a high-oxygen background, is compared by discussing experimental data (i.e. low-energy electron diffraction, scanning tunneling microscopy) and density functional theory calculations. Two rectangular phases, called rect-TiO(2) and rect'-TiO(2) were obtained on both the hexagonal Pt(111) and the rectangular (1x2)-Pt(110) substrates, generally suggesting that they are weakly interacting with the substrates. The rect-TiO(2) phase is actually confined to a TiO(2) double layer, while the rect'-TiO(2) can extend up to a thickness of several layers and is obtained when higher Ti doses are evaporated. While the rect-TiO(2) is best described as a thickness-limited lepidocrocite-like nanosheet, growing as a single-domain-commensurate (14x4) phase on (1x2)-Pt(110) and as a six-domains-incommensurate phase on Pt(111), the thicker rect'-TiO(2) phase can be best described as a TiO(2)(B) supported nanolayer (NL). This represents the first example of the TiO(2)(B) phase in the form of a supported NL, whose properties are still largely unexplored. The important point is that, because of the weak interaction between the oxide NLs and the Pt surfaces, the substrate does not play a role in stabilizing the 2D nanostructures. Rather, it acts as a sort of lab bench where sub-nanosized titania crystallites self-assemble, so that the final NLs are representative of 2D confined titania at the bottom of the nanoscale.