Large area (1 mm2) vertical NiO/β n-Ga2O/n+ Ga2O3 heterojunction rectifiers are demonstrated with simultaneous high breakdown voltage and large conducting currents. The devices showed breakdown voltages (VB) of 3.6 kV for a drift layer doping of 8 x 1015 cm-3, with 4.8 A forward current. This performance is higher than the unipolar 1D limit for GaN, showing the promise of β-Ga2O3 for future generations of high-power rectification devices. The breakdown voltage was a strong function of drift region carrier concentration, with VB dropping to 1.76 kV for epi layer doping of 2 x 1016 cm-3. The power figure-of-merit, VB2/RON, was 8.64 GW·cm-2, where RON is the on-state resistance (1.5 mΩ.cm2). The on-off ratio switching from 12 to 0 V was 2.8 x 1013, while it was 2 x 1012 switching from 100 V. The turn-on voltage was 1.8 V. The reverse recovery time was 42 ns, with a reverse recovery current of 34 mA.