Integrating　monoclinic　gallium　oxide　(R-Ga2O3)　with　two-dimensional　(2D)　hexagonal　boron　nitride　(h-BN)　into　heterostructures　is　of　significant　importance　for　achieving　high-　power　device　applications.　The　2D-material-assisted　epitaxy　provides　a　straightforward　integration　method　for　fabricating　R-Ga2O3/h-BN　vertical　heterostructures.　In　this　work,　the　R-Ga2O3　films　were　deposited　on　both　polycrystalline　and　single-crystalline　h-BN　layers　with　different　thicknesses,　and　two　growth　modes　of　R-Ga2O3　films　on　h-BN,　remote　epitaxy,　and　van　der　Waals　(vdW)　epitaxy,　were　investigated.　The　results　show　that　the　potential　of　the　sapphire　substrate　can　penetrate　the　monolayer　and　bilayer　h-BN　to　obtain　the　remote　epitaxy　of　R-Ga2O3　films,　regardless　of　the　crystallinity　of　h-BN.　The　vdW　epitaxy　of　R-Ga2O3　film　can　be　realized　on　the　monocrystalline　h-BN　substrate.　Compared　with　the　conventional　and　remote　epitaxial　R-Ga2O3　films　on　sapphire　substrate,　the　vdW　epitaxial　R-Ga2O3　films　on　the　single-　crystalline　h-BN　substrate　exhibit　higher　crystallinity.　This　work　indicates　that　the　2D-material-assisted　epitaxy　provides　a　feasible　scheme　for　the　heterogeneous　integration　of　R-Ga2O3　films.