Segregation veins are common in lava sheets and result from internal differentiation during lava emplacement and degassing. They consist of evolved liquid, most likely replaced by gas-filter pressing from a ∼50% crystallised host lava. Pairs of samples, host lavas and associated segregation veins from the Reykjanes Peninsula (Iceland), Lanzarote (Canary Islands) and the Masaya volcano (Nicaragua) show extreme mineralogical and compositional variations (MgO in host lava, segregation veins and interstitial glass ranges from 8–10 wt%, 3–6 wt%, and to less than 0.01 wt%, respectively). These samples allow the assessment of the internal lava flow differentiation mechanism, since both the parental and derived liquid are known in addition to the last magma drops in the form of late interstitial glasses. The mineralogical variation, mass-balance calculated from major- and trace element composition, and transitional metal partition between crystals and melts are all consistent with fractional crystallisation as the dominant differentiation mechanism. The interstitial glasses are highly silicic (SiO₂ = 70–80 wt%) and represent a final product of high-degree (75–97%) fractional crystallisation of olivine tholeiite at a pressure close to one atmosphere. The tholeiitic liquid-line-of-decent and the composition of the residual melts are governed by the K₂O/Na₂O of the initial basaltic magma. The granitic minimum is reached if the initial liquid has a high K₂O/Na₂O whereas trondhjemitic composition is the final product of magma with low initial K₂O/Na₂O.