  We present theoretical studies of morphology, stability, and electronic
structure of monolayer hexagonal CBN alloys with rich content of h-BN and
carbon concentration not exceeding 50 %. Our studies are based on the bond
order type of the valence force field to account for the interactions between
atomic constituents and Monte Carlo method with Metropolis algorithm to
establish equilibrium distribution of atoms over the lattice. We find out that
the phase separation into graphene and h-BN domains occurs in the majority of
growth conditions. Only in N-rich growth conditions, it is possible to obtain
quasi uniform distribution of carbon atoms over boron sublattice. We predict
also that the energy gap in stoichiometric C$_x$(BN)$_{1-x}$ alloys exhibits
extremely strong bowing.
