Continental rifts and passive continental margins show fundamental along‐axis segmentation patterns that have been attributed to one or a number of different processes: extensional fault geometry, variable stretching along strike, preexisting lithospheric compositional and structural heterogeneities, oblique rifting, and the presence or absence of eruptive volcanic centers. The length and width scales of the rift stage fault‐bounded basin systems change during the late evolution of the new plate boundary, and the role of magmatism may increase as rifting progresses to continental rupture. Along obliquely spreading ridges, first‐order mid‐ocean ridge geometries originate during the synrift stage, indicating an intimate relationship between magma production and transform fault spacing and location. The Gulf of Aden rift is a young ocean basin in which the earliest synrift to breakup structures are well exposed onshore and covered by thin sediment layers offshore. This obliquely spreading rift is considered magma‐poor and has several large‐offset transforms that originated during late stage rifting and control the first‐order axial segmentation of the spreading ridge. Widely spaced geophysical transects of passive margins that produce only isolated 2‐D images of crust and uppermost mantle structure are inadequate for evaluation of competing rift evolution models. Using closely spaced new geophysical and geological observations from the Gulf of Aden we show that rift sectors between transforms have a large internal variability over short distances (∼10 km): the ocean‐continent transition (OCT) evolves from a narrow magmatic transition to wider zones where continental mantle is probably exhumed. We suggest that this small‐scale variability may be explained (1) by the distribution of volcanism and (2) by the along‐strike differences in time‐averaged extension rate of the oblique rift system. The volcanism may be associated with (1) the long‐offset Alula‐Fartak Fracture Zone, which may enhance magma production on its younger side, or (2) channeled flow from the Afar plume material along the newly formed OCT and the spreading ridge. Oblique extension and/or hot spot interactions may thereby have a significant control on the styles of rifting and continental breakup and on the evolution of many magma‐poor margins.