We highlight with first-principles molecular dynamics the persistence of intrinsic 〈111〉 Ti off-centerings for BaTiO_{3} in its cubic paraelectric phase. Intriguingly, these are inconsistent with the Pm3[over ¯]m space group often used to atomistically model this phase using density-functional theory or similar methods. Therefore, we deploy a systematic symmetry analysis to construct representative structural models in the form of supercells that satisfy a desired point symmetry but are built from the combination of lower-symmetry primitive cells. We define as structural prototypes the smallest of these that are both energetically and dynamically stable. Remarkably, two 40-atom prototypes can be identified for paraelectric BaTiO_{3}; these are also common to many other ABO_{3} perovskites. These prototypes can offer structural models of paraelectric phases that can be used for the computational engineering of functional materials. Last, we show that the emergence of B-cation off-centerings and the primitive-cell phonon instabilities is controlled by the equilibrium volume, in turn, dictated by the filler A cation.