The widespread Lago-Mare facies show that the Mediterranean was fully isolated from the World Ocean at the end of the Messinian salinity crisis (MSC): the Plio-Quaternary Gibraltar Strait has no geographical feature in common with the Miocene Portals, which were continentalised before the end of the MSC. A copy of a budget model has been modified to study the infilling of the Mediterranean. The yearly Atlantic water supply follows an exponential increase law. The level of the basins does not change significantly during the 26 early years, but the refill of the Mediterranean basins is completed within the next 10-11 years. The high velocity of the flow of Atlantic water can be reconfirmed by hydraulic calculations. The morphological study of the area suggests that the Gibraltar Strait originates from an eastwards flowing stream, which drained the eastern slope of an emergent Gibraltar Isthmus to the Mediterranean Basins at the end of the Messinian. Similar canyons are still found in the marine topography towards the Alboran Sea. The present Spartel and Camarinal Sills both originate from the coeval mass sliding of the northern bank of the strait. The strait of Gibraltar results from the work of a stream, which managed water-piracy from an Ocean.