We suggest the 550 km long Terceira Rift (Azores Plateau) is the world's slowest-spreading (hyper-slow, 4 mm/a plate separation; 2.3-3.8 mm/a perpendicular to oblique axial segments) organized accreting plate boundary. In its slightly sinuous (ca. 300 km radius of curvature) axial trace, its oblique spreading angles (ca. 40°-65°), and in frequency and first motions of earthquakes, the TR resembles better-known ultra- or super- slow spreading ridges (e.g., Gakkel and Southwest Indian ridges). Interpreted simply as volcanically unfilled rift valley segments, the inter-island basins (e.g., the 3200 m deep Hirondelle Basin) are slightly wider (30-60 km), but not significantly deeper (1000-2200 m) than the Mid-Atlantic Ridge median valley (20-28 mm/a; 10°N-53°N). However, along-axis segmentation wavelengths (ca. 100 km) are double those along the central MAR, but make TR comparable to the ultra-slow (15-16 mm/a) Southwest Indian and Gakkel (7-13 mm/a) ridges. If this segmentation wavelength reflects Rayleigh-Taylor instabilities, the viscosity contrast between the overlying axial lithosphere and the partial melt zones is about an order of magnitude greater at ca. 4-16 mm/a than at 20-30 mm/a. The Terceira Rift differs dramatically from ultra-slow ridges only in the large amplitude of along-strike topography (2000-4000 m; 4200 m total variation) owing perhaps to a copious melt flux from the Azores hotspot, combined with a spreading-rate-determined greater axial flexural strength and plate thickness, and slower export of volcanics from the rift axis. The probable TR youth (ca. 1 Ma, requiring less than 4 km new oceanic crust) indicates lack of steady-state spreading conditions, which may explain the published gravity evidence against TR spreading. Absolute plate motions support the creation of the Azores Plateau by successive NE jumps of the rift axis to maintain its position over a fixed hotspot.