  In the classic type I seesaw mechanism with very heavy right-handed (RH)
neutrinos, it is possible to account for dark matter via RH neutrino portal
couplings to a feebly interacting massive particle (FIMP) dark sector. However,
for large RH neutrino masses, gravity can play an important role. We study the
interplay between the neutrino portal through the right-handed neutrinos and
the gravity portal through the massless spin-2 graviton in producing dark
matter particles in the early universe. As a concrete example, we consider the
minimal and realistic Littlest Seesaw model with two RH neutrinos, augmented
with a dark scalar and a dark fermion charged under a global $U(1)_D$ dark
symmetry. In the model, the usual seesaw neutrino Yukawa couplings and the
right-handed neutrino masses (the lightest being about $5\times 10^{10}$ GeV)
are fixed by neutrino oscillations data and leptogenesis. Hence, we explore the
parameter space of the two RH neutrino portal couplings, the two dark particle
masses and the reheating temperature of the universe, where the correct dark
matter relic abundance is achieved through the freeze-in mechanism. In
particular, we highlight which class of processes dominate the dark matter
production. We find that, despite the presence of the gravity portal, the dark
matter production relies on the usual seesaw neutrino Yukawa coupling in some
regions of the parameter space, so realising a direct link between dark matter
and neutrino phenomenology. Finally, we report the threshold values for the
neutrino portal couplings below which the neutrino portal is irrelevant and the
Planckian Interacting Dark Matter paradigm is preserved.
