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When continents rift to form new ocean basins, the rifting is sometimes accompanied by massive igneous activity. We show that the production of magmatically active rifted margins and the effusion of flood basalts onto the adjacent continents can be explained by a simple model of rifting above a thermal anomaly in the underlying mantle. The igneous rocks are generated by decompression melting of hot asthenospheric mantle as it rises passively beneath the stretched and thinned lithosphere. Mantle plumes generate regions beneath the lithosphere typically 2000 km in diameter with temperatures raised 100–200°C above normal. These relatively small mantle temperature increases are sufficient to cause the generation of huge quantities of melt by decompression: an increase of 100°C above normal doubles the amount of melt whilst a 200°C increase can quadruple it. In the first part of this paper we develop our model to predict the effects of melt generation for varying amounts of stretching with a range of mantle temperatures. The melt generated by decompression migrates rapidly upward, until it is either extruded as basalt flows or intruded into or beneath the crust. Addition of large quantities of new igneous rock to the crust considerably modifies the subsidence in rifted regions. Stretching by a factor of 5 above normal temperature mantle produces immediate subsidence of more than 2 km in order to maintain isostatic equilibrium. If the mantle is 150°C or more hotter than normal, the same amount of stretching results in uplift above sea level. Melt generated from abnormally hot mantle is more magnesian rich than that produced from normal temperature mantle. This causes an increase in seismic velocity of the igneous rocks emplaced in the crust, from typically 6.8 km/s for normal mantle temperatures to 7.2 km/s or higher. There is a concomitant density increase. In the second part of the paper we review volcanic continental margins and flood basalt provinces globally and show that they are always related to the thermal anomaly created by a nearby mantle plume. Our model of melt generation in passively upwelling mantle beneath rifting continental lithosphere can explain all the major rift-related igneous provinces. These include the Tertiary igneous provinces of Britain and Greenland and the associated volcanic continental margins caused by opening of the North Atlantic in the presence of the Iceland plume; the Paraná and parts of the Karoo flood basalts together with volcanic continental margins generated when the South Atlantic opened; the Deccan flood basalts of India and the Seychelles-Saya da Malha volcanic province created when the Seychelles split off India above the Réunion hot spot; the Ethiopian and Yemen Traps created by rifting of the Red Sea and Gulf of Aden region above the Afar hot spot; and the oldest and probably originally the largest flood basalt province of the Karoo produced when Gondwana split apart. New continental splits do not always occur above thermal anomalies in the mantle caused by plumes, but when they do, huge quantities of igneous material are added to the continental crust. This is an important method of increasing the volume of the continental crust through geologic time.