PbHfO(3) is investigated theoretically and experimentally with respect to possible precursor effects starting in the paraelectric phase far above the cubic to tetragonal phase transition temperature. The theoretical modeling within the polarizability model predicts a giant softness of the system with spatially large polar and antiferrodistortive domain formation which compete with each other. These predictions are substantiated by the experiments, where the softness and the precursor effects are confirmed by birefringence, dielectric permittivity measurements and elastic properties by Brillouin scattering. The intermediate phase is found to have the polar nature confirmed by P-E hysteresis loop measurements, which is another manifestation of the competition between interrelated instabilities, namely a polar one and an antiferroelectric one.