A tectonic model of the evolution of the northern half of the South Fiji Basin, including the Minerva Triple Junction and Cook Fracture Zone, is developed from regional gravity, multibeam bathymetry, and a new interpretation of magnetic anomalies pinned to radiometric dates of oceanic crust in the basin. The geometry and age of a portion of the Minerva Triple Junction and the Cook-Minerva spreading center (the connection from the triple junction to the Cook Fracture Zone, which accommodated coeval opening of the Norfolk Basin), are resolved with multibeam bathymetry and magnetics. The South Fiji Basin opened from about 34 to 15 Ma in an anticlockwise sweep about an Euler pole located at the northern end of the present Lau Ridge. This rotation and a rigidly straight southeastward motion of the Three Kings Ridge were accommodated by the configuration of the triple junction changing from ridge-fault-fault to ridge-ridge-fault to ridge-ridge-ridge. During this evolution the southeastern arm of the system, the Julia Fracture Zone, underwent several transformations and the Cook-Minerva spreading center experienced repeated ridge jumps. The kinematics of the northern South Fiji Basin dictate, to a large extent, the evolution of the southern South Fiji Basin and the Norfolk Basin. This in turn leads to the interpretation of a complex trench-trench-double transform fault framework at the northern New Zealand margin, which explains most aspects of the geology, structure, and arc volcanic history of the margin and provides a radical new setting for the origin of the Northland Allochthon.