  We present a theoretical study of electronic and thermal transport in
polycrystalline heterostructures combining graphene (G) and hexagonal boron
nitride (hBN) grains of varying size and distribution. By increasing the hBN
grain density from a few percents to $100\%$, the system evolves from a good
conductor to an insulator, with the mobility dropping by orders of magnitude
and the sheet resistance reaching the M$\Omega$ regime. The Seebeck coefficient
is suppressed above $40\%$ mixing, while the thermal conductivity of
polycrystalline hBN is found to be on the order of $30-120\,{\rm W}{\rm
m}^{-1}{\rm K}^{-1}$. These results, agreeing with available experimental data,
provide guidelines for tuning G-hBN properties in the context of
two-dimensional materials engineering. In particular, while we proved that both
electrical and thermal properties are largely affected by morphological
features (like e.g. by the grain size and composition), we find in all cases
that nm-sized polycrystalline G-hBN heterostructures are not good
thermoelectric materials.
