  The South Atlantic rift basin evolved as branch of a large
Jurassic-Cretaceous intraplate rift zone between the African and South American
plates during the final breakup of western Gondwana. By quantitatively
accounting for crustal deformation in the Central and West African rift zone,
we indirectly construct the kinematic history of the pre-breakup evolution of
the conjugate West African-Brazilian margins. Our model suggests a causal link
between changes in extension direction and velocity during continental
extension and the generation of marginal structures such as the enigmatic
Pre-salt sag basin and the S\~ao Paulo High. We model an initial E-W directed
extension between South America and Africa (fixed in present-day position) at
very low extensional velocities until Upper Hauterivian times ($\approx$126 Ma)
when rift activity along in the equatorial Atlantic domain started to increase
significantly. During this initial $\approx$17 Myr-long stretching episode the
Pre-salt basin width on the conjugate Brazilian and West African margins is
generated. An intermediate stage between 126.57 Ma and Base Aptian is
characterised by strain localisation, rapid lithospheric weakening in the
equatorial Atlantic domain, resulting in both progressively increasing
extensional velocities as well as a significant rotation of the extension
direction to NE-SW. Final breakup between South America and Africa occurred in
the conjugate Santos--Benguela margin segment at around 113 Ma and in the
Equatorial Atlantic domain between the Ghanaian Ridge and the Piau\'i-Cear\'a
margin at 103 Ma. We conclude that such a multi-velocity, multi-directional
rift history exerts primary control on the evolution of this conjugate passive
margins systems and can explain the first order tectonic structures along the
South Atlantic and possibly other passive margins.
