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Summary * This paper is the first global study of the extent to which fire determines global vegetation patterns by preventing ecosystems from achieving the potential height, biomass and dominant functional types expected under the ambient climate (climate potential). * To determine climate potential, we simulated vegetation without fire using a dynamic global-vegetation model. Model results were tested against fire exclusion studies from different parts of the world. Simulated dominant growth forms and tree cover were compared with satellite-derived land- and tree-cover maps. * Simulations were generally consistent with results of fire exclusion studies in southern Africa and elsewhere. Comparison of global 'fire off' simulations with landcover and treecover maps show that vast areas of humid C4 grasslands and savannas, especially in South America and Africa, have the climate potential to form forests. These are the most frequently burnt ecosystems in the world. Without fire, closed forests would double from 27% to 56% of vegetated grid cells, mostly at the expense of C4 plants but also of C3 shrubs and grasses in cooler climates. * C4 grasses began spreading 6–8 Ma, long before human influence on fire regimes. Our results suggest that fire was a major factor in their spread into forested regions, splitting biotas into fire tolerant and intolerant taxa.