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The future rate of Greenland Ice Sheet (GrIS) deglaciation and the future contribution of GrIS deglaciation to sea level rise will depend critically on the magnitude of northern hemispheric polar amplification and global equilibrium climate sensitivity. Here, these relationships are analyzed using an ensemble of multi-century coupled ice-sheet/climate model simulations seeded with observationally-constrained initial conditions and then integrated forward under tripled preindustrial CO. Polar amplifications and climate sensitivities were varied between ensemble members in order to bracket current uncertainty in polar amplification and climate sensitivity. A large inter-ensemble spread in mean GrIS air temperature, albedo and surface mass balance trends stemming from this uncertainty resulted in GrIS ice volume loss ranging from 5 to 40 % of the original ice volume after 500 years. The large dependence of GrIS deglaciation on polar amplification and climate sensitivity that we find indicates that the representation of these processes in climate models will exert a strong control on any simulated predictions of multi-century GrIS evolution. Efforts to reduce polar amplification and equilibrium climate sensitivity uncertainty will therefore play a critical role in constraining projections of GrIS deglaciation and sea level rise in a future high-CO world. [ABSTRACT FROM AUTHOR]