  The complete set of transport coefficients for two dimensional relativistic
degenerate gases is derived within a relaxation approximation in kinetic
theory, by considering both the particle and energy frames. A thorough
comparison between Marle and Anderson-Witting's models is carried out, pointing
out the drawbacks of the former when compared both to the latter and to the
full Boltzmann equation results in the non-degenerate limit. Such task is
accomplished by solving the relativistic Uehling-Uhlenbeck equation, in both
the particle and energy frames, in order to establish the constitutive
equations for the heat flux and the Navier tensor together with analytical
expressions for the transport coefficients in such representations. In
particular, the temperature dependence of the thermal conductivity (associated
with a generalized thermal force) and the bulk and shear viscosities are
analyzed and compared within both models and with the non-degenerate,
non-relativistic and ultra-relativistic limits.
