A measurement of the analyzing powers for the H-2((p) over bar ,pp)n break-up reaction was carried out at KVI exploiting a polarized-proton beam at an energy of 135MeV. The scattering angles and energies of the final-state protons were measured using the Big Instrument for Nuclear-polarization Analysis (BINA) with a nearly 4 pi geometrical acceptance. In this work, we analyzed a large number of kinematical geometries including forward-forward configurations in which both the final-state particles scatter to small polar angles and backward-forward configurations in which one of the final-state particles scatters to large polar angles. The results are compared with Faddeev calculations based on modern nucleon-nucleon (NN) and three-nucleon (3N) potentials. Discrepancies between polarization data and theoretical predictions are observed for configurations corresponding to small relative azimuthal angles between the two final-state protons. These configurations show a large sensitivity to 3N force effects.