The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power law distribution suggested by the nonextensive kinetic theory. There are two different classes of solutions. The first class behaves like a subset of the polytropic Lane-Emden spheres, whereas the second one corresponds to a transition between two different polytropic indices. Unlike the isothermal Maxwellian sphere, the total mass and sizes of both classes are finite for a large range of the nonextensive q-parameter
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