The geometry of the Antarctic-Phoenix Plate system, with the Antarctic Plate forming both the overriding plate and the conjugate to the subducting oceanic plate, allows quantification of slab age and convergence rate back to the Paleocene and direct comparison with the associated magmatic arc. New Ar-Ar data from Cape Melville (South Shetland Islands, SSI) and collated geochronology shows Antarctic arc magmatism ceased at ~19 Ma. Since the Cretaceous, the arc front remained ~100 km from the trench whilst its rear migrated trenchward at 6 km/Myr. South of the SSI, arc magmatism ceased ~8–5 Myr prior to each ridge-trench collision, whilst on the SSI (where no collision occurred) the end of arc magmatism predates the end of subduction by ~16 Myr. Despite the narrowing and successive cessation of the arc, geochemical and dyke orientation data shows the arc remained in a consistently transitional state of compressional continental arc and extensional backarc tectonics. Numerically relating slab age, convergence rate, and slab dip to the Antarctic-Phoenix Plate system, we conclude that the narrowing of the arc and the cessation of magmatism south of the South Shetland Islands was primarily in response to the subduction of progressively younger oceanic crust, and secondarily to the decreasing convergence rate. Increased slab dip beneath the SSI migrated the final magmatism offshore. Comparable changes in the geometry and composition are observed on the Andean arc, suggesting slab age and convergence rate may affect magmatic arc geometry and composition in settings currently attributed to slab dip variation.