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Many simulations have been devoted to study the impact of global desertification on climate, but very few have quantified this impact in very different climate contexts. Here, the climatic impacts of large-scale global desertification in warm (2100 under the SRES A2 scenario forcing), modern and cold (Last Glacial Maximum, 21 thousand years ago) climates are assessed by using the IPSL OAGCM. For each climate, two simulations have been performed, one in which the continents are covered by modern vegetation, the other in which global vegetation is changed to desert i.e. bare soil. The comparison between desert and present vegetation worlds reveals that the prevailing signal in terms of surface energy budget is dominated by the reduction of upward latent heat transfer. Replacing the vegetation by bare soil has similar impacts on surface air temperature South of 20 degrees N in all three climatic contexts, with a warming over tropical forests and a slight cooling over semi-arid and arid areas, and these temperature changes are of the same order of magnitude. North of 20 degrees N, the difference between the temperatures simulated with present day vegetation and in a desert world is mainly due to the change in net radiation related to the modulation of the snow albedo by vegetation, which is obviously absent in the desert world simulations. The enhanced albedo in the desert world simulations induces a large temperature decrease, especially during summer in the cold and modern climatic contexts, whereas the largest difference occurs during winter in the warm climate. This temperature difference requires a larger heat transport to the northern high latitudes. Part of this heat transport increase is achieved through an intensification of the Atlantic Meridional Overturning Circulation. This intensification reduces the sea-ice extent and causes a warming over the North Atlantic and Arctic oceans in the warm climate context. In contrast, the large cooling North of 20 degrees N in both the modern and cold climate contexts induces an increase in sea-ice extent.