We investigated the Cretaceous Potiguar Basin in the Equatorial margin of Brazil to understand how the geometry of major faults evolved to form the basin internal architecture. Previous studies pointed out that the rift is an asymmetrical half-graben elongated along the NE-SW direction. We used 2D seismic, well logs and 3D gravity modeling to analyze faults that constitute the rift boundary and determine their maximum displacement (D_max) and length (L) ratio in the Potiguar Rift. We constrained the 3D gravity modeling with well data and the interpretation of seismic sections. The difference of the fault displacement and depth of the basement obtained in the gravity model is in the order of 10% compared to seismic and well data. The fault-growth curves allowed us to divide the faulted rift border into four main fault systems, which provide roughly similar D_max/L ratios. Fault-growth curves suggest that a regional uniform tectonic mechanism influenced growth of these faults. These fault systems are composed of minor faults that we define as segments. The variation of the displacements along the fault segments indicates that the fault systems were formed independently during rift initiation and were linked by hard and soft linkages. The latter formed relay ramps. In the interconnection zones the D_max/L ratios are highest due to interference of fault segment motions. We divided the evolution of the Potiguar Rift into five stages based on these ratios and correlated them with the major tectonic stages of the breakup between South America and Africa in the Early Cretaceous.