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Abstract: The Patagonian slab window is a subsurface tectonic feature resulting from subduction of the Nazca–Antarctic spreading-ridge system (Chile Rise) beneath southern South America. The geometry of the slab window had not been rigorously defined, in part because of the complex nature of the history of ridge subduction in the southeast Pacific region, which includes four interrelated spreading-ridge systems since 20 Ma: first, the Nazca–Phoenix ridge beneath South America, then simultaneous subduction of the Nazca–Antarctic and the northern Phoenix–Antarctic spreading-ridge systems beneath South America, and the southern Phoenix–Antarctic spreading-ridge system beneath Antarctica. Spreading-ridge paleo-geographies and rotation poles for all relevant plate pairs (Nazca, Phoenix, Antarctic, South America) are available from 20 Ma onward, and form the mathematical basis of our kinematic reconstruction of the geometry of the Patagonia and Antarctic slab windows through Neogene time. At approximately 18 Ma, the Nazca–Phoenix–Antarctic oceanic (ridge–ridge–ridge) triple junction enters the South American trench; we recognize this condition as an unstable quadruple junction. Heat flow at this junction and for some distance beneath the forearc would be considerably higher than is generally recognized in cases of ridge subduction. From 16 Ma onward, the geometry of the Patagonia slab window developed from the subduction of the trailing arms of the former oceanic triple junction. The majority of the slab window''s areal extent and geometry is controlled by the highly oblique (near-parallel) subduction angle of the Nazca–Antarctic ridge system, and by the high contrast in relative convergence rates between these two plates relative to South America. The very slow convergence rate of the Antarctic slab is manifested by the shallow levels achieved by the slab edge (<45 km); thus no point on the Antarctic slab is sufficiently deep to generate “normal” mantle-derived arc-type magmas. Upwelling beneath the region may have contributed to uplift and eastward transfer of extension in the Scotia Sea. [Copyright &y& Elsevier]