  We introduce a new phase space representation for open quantum systems. This
is a very powerful tool to help advance in the study of the morphology of their
eigenstates. We apply it to two different versions of a paradigmatic model, the
baker map. This allows to show that the long-lived resonances are strongly
scarred along the shortest periodic orbits that belong to the classical
repeller. Moreover, the shape of the short-lived eigenstates is also analyzed.
Finally, we apply an antiunitary symmetry measure to the resonances that
permits to quantify their localization on the repeller.
