The western quarter of North America consists of accreted terranes--crustal blocks added over the past 200 million years--but the reason for this is unclear. The widely accepted explanation posits that the oceanic Farallon plate acted as a conveyor belt, sweeping terranes into the continental margin while subducting under it. Here we show that this hypothesis, which fails to explain many terrane complexities, is also inconsistent with new tomographic images of lower-mantle slabs, and with their locations relative to plate reconstructions. We offer a reinterpretation of North American palaeogeography and test it quantitatively: collision events are clearly recorded by slab geometry, and can be time calibrated and reconciled with plate reconstructions and surface geology. The seas west of Cretaceous North America must have resembled today's western Pacific, strung with island arcs. All proto-Pacific plates initially subducted into almost stationary, intra-oceanic trenches, and accumulated below as massive vertical slab walls. Above the slabs, long-lived volcanic archipelagos and subduction complexes grew. Crustal accretion occurred when North America overrode the archipelagos, causing major episodes of Cordilleran mountain building.