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Despite the decade-long study of the effect of nanoconfinement on the glass-transition temperature (T_g) of amorphous materials, the quest to probe the distribution of T_gs in nanoconfined glass formers has remained unfulfilled. Here the distribution of T_gs across polystyrene films has been obtained by a fluorescence/multilayer method, revealing that the enhancement of dynamics at a surface affects T_g several tens of nanometres into the film. The extent to which dynamics smoothly transition from enhanced to bulk states depends strongly on nanoconfinement. When polymer films are sufficiently thin that a reduction in thickness leads to a reduction in overall T_g, the surface-layer T_g actually increases with a reduction in overall thickness, whereas the substrate-layer T_g decreases. These results indicate that the gradient in T_g dynamics is not abrupt, and that the size of a cooperatively rearranging region is much smaller …