  We develop a complete description of the class of conformal relativistic
dissipative fluids of divergence form, following the formalism carried out by
Geroch, Lindblom and Pennisi. This type of theories is fully described in terms
of evolution variables whose dynamics is governed by total divergence-type
conservation laws. Specifically, we give a characterization of the whole family
of conformal fluids in terms of a single master scalar function defined up to
second order corrections in dissipative effects, which we explicitly find in
general form. This allows us to identify the equilibrium states of the theory,
as well as to derive constitutive relations and a Fourier-like law for the
corresponding first-order theory heat flux. Finally, we show that among this
class of theories-- and near equilibrium configurations-- there exist symmetric
hyperbolic ones, implying that for them one can define well posed initial value
problems.
