We study the genesis of dark matter in the primordial Universe for representative classes of Z′-portals models. For weak-scale Z′ mediators we compute the range of values of the kinetic mixing allowed by WMAP/PLANCK experiments corresponding to a FIMP regime. We show that very small values of δ (10−12≲δ≲10−11) are sufficient to produce the right amount of dark matter. We also analyse the case of very massive gauge mediators, whose mass mZ′ is larger than the reheating temperature, TRH, with a weak-scale coupling gD to ordinary matter. Relic abundance constraints then impose a direct correlation between TRH and the effective scale Λ of the interactions: Λ ∼ 103−105 × TRH. Finally we describe in some detail the process of dark thermalisation and study its consequences on the computation of the relic abundance.