  We study a sub monolayer He-4 adsorbed on fluorographene (GF) and on
hexagonal boron nitride (hBN) at low coverage. The adsorption potentials have
been computed ab-initio with a suitable density functional theory including
dispersion forces. The properties of the adsorbed He-4 atoms have been computed
at finite temperature with path integral Monte Carlo and at T=0 K with
variational path integral. From both methods we find that the lowest energy
state of He-4 on GF is a superfluid. Due to the very large corrugation of the
adsorption potential this superfluid has a very strong spatial anisotropy, the
ratio between the largest and smallest areal density being about 6. Thus, GF
offers a platform for studying the properties of a strongly interacting highly
anisotropic bosonic superfluid. At a larger coverage He-4 has a transition to
an ordered commensurate state with occupation of 1/6 of the adsorption sites.
The system has a triangular order similar to that of He-4 on graphite but each
He-4 atom is not confined to a single adsorption site and the atom visits also
the nearest neighboring sites giving rise to a novel three--lobed density
distribution. The lowest energy state of He-4 on hBN is an ordered commensurate
state with occupation of 1/3 of the adsorption sites and triangular symmetry. A
disordered state is present at lower coverage as a metastable state. In
presence of an electric field the corrugation of the adsorption potential is
slightly increased but up to a magnitude of 1 V/Ang the effect is small and
does not change the stability of the phases of He-4 on GF and hBN. We have
verified that also in the case of graphene such electric field does not modify
the stability of the commensurate sqrt(3)*sqrt(3)R30 phase.
