6 pages, 3 figuresThe concept of black hole entropy is one of the most important enigmas of theoretical physics. It relates thermodynamics to gravity and allows substantial hints toward a quantum theory of gravitation. Although Bekenstein conjecture -assuming the black hole entropy to be a measure of the number of precollapse configurations- has proved to be extremely fruitful, a direct and conclusive proof is still missing. This article computes accurately the entropy evaporated by black holes in (4+n) dimensions taking into account the exact greybody factors. This is a key process to constrain and understand the entropy of black holes as the final state is unambiguously defined. Those results allow to generalize Zurek's important argument...