  The popular freeze-out paradigm for Dark Matter (DM) production, relies on
DM-baryon couplings of the order of the weak interactions. However, different
search strategies for DM have failed to provide a conclusive evidence of such
(non-gravitational) interactions, while greatly reducing the parameter space of
many representative models. This motivates the study of alternative mechanisms
for DM genesis. In the freeze-in framework, the DM is slowly populated from the
thermal bath while never reaching equilibrium. In this work, we analyse in
detail the possibility of producing a frozen-in DM via a mediator particle
which acts as a portal. We give analytical estimates of different freeze-in
regimes and support them with full numerical analyses, taking into account the
proper distribution functions of bath particles. Finally, we constrain the
parameter space of generic models by requiring agreement with DM relic
abundance observations.
