We present first-principles calculations of vanadia-titania catalysts at V-coverages up to one monolayer. Realistic slab models are built where vanadate species (VOx) are grafted onto hydroxyls existing at the (001) surfaces exposed by the TiO2-anatase support. The structure and stability of several microscopic models of oxidized VOx (sub)monolayers have been computed. We find that tetrahedrally coordinated monovanadate units are stable for low V-coverages, but are readily converted to divanadate units for higher coverages. The structure of these units is closely related to that of a recently proposed model of the (1 x 4) reconstruction of the dehydroxylated (001) anatase surface, where arrays of surface bridging oxygens are replaced by tetrahedral structures. High V-coverages (>0.5 ML) can be obtained if the substrate acquires the structure of a bulk-terminated TiO2(001) surface. In this case, a stable polymeric structure can be formed, which is structurally related to a (100)-oriented vanadia layer. At the same time, the coordination around the V atoms changes from four to five, in agreement with experiment. Thick vanadia layers are found to be unstable with respect to decomposition into separate supported-monolayer and bulk vanadia phases.