  An ergodic dynamical system $\mathbf{X}$ is called dominant if it is
isomorphic to a generic extension of itself. It was shown in an earlier paper
by Glasner, Thouvenot and Weiss that Bernoulli systems with finite entropy are
dominant. In this work we show first that every ergodic system with positive
entropy is dominant, and then that if $\mathbf{X}$ has zero entropy then it is
not dominant.
