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We show explicitly that the one- and two-dimensional Hubbard model does notshow phase separation at any filling at T=0. Apart from a single plausibleassumption, only known exact results and symmetry properties for the one-bandHubbard model are used. Implications for usage of the simple one-band Hubbardmodel for analysing the physics of cuprate superconductors are discussed. Wealso discuss models where electronic phase separation might generically occur,in the specific context of colossal magneto-resistance manganites.

On the Impossibility of Electronic Phase Separation in the $D=1,2$ Dimensional Hubbard Model at T=0