  In recent works (BHP), a generalized universality has been proposed, linking
phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we
performed a MC study of the 2D XY-model. We found that the shape of the
probability distribution function for the magnetization M is non Gaussian and
independent of the system size --in the range of the lattice sizes studied--
below the Kosterlitz-Thoules temperature. However, the shape of these
distributions does depend on the temperature, contrarily to the BHP's claim.
This behavior is successfully explained by using an extended finite-size
scaling analysis and the existence of bounds for M.
