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Segmental copy-number gains are major contributors to human genetic variation and disease, but how these alterations arise remains incompletely understood. Here, based on the analyses of both experimental evolution and human disease genomes, we describe a general mechanism of segmental copy-number gain from a rearrangement process termed 'breakage-replication/fusion'. The hallmark genomic feature of breakage-replication/fusion is adjacent parallel breakpoints: two or more rearrangement breakpoints derived from replication of a single ancestral DNA end. We show that adjacent parallel breakpoints are a widespread feature of DNA duplications in human disease genomes and experimental models of chromothripsis. In addition to adjacent parallel breakpoints, breakage-replication/fusion also explains two other patterns of complex rearrangements with unclear provenance: chains of short (≤1 kb) insertions and high-level amplification consisting of inverted segments. Together, these findings revise the mechanistic model for chromothripsis and provide a new conceptual framework for understanding the origin of segmental DNA duplication during genome evolution.