Reliable　transfer　techniques　are　critical　for　the　integration　of　2D　materials　with　arbitrary　substrates.　Here,　the　authors　describe　a　method　to　transfer　4-inch　and　A4-sized　defect-free　graphene　films　onto　rigid　and　flexible　substrates　with　controllable　conformal　contact,　leading　to　improved　electrical　properties　and　uniformity.　The　availability　of　graphene　and　other　two-dimensional　(2D)　materials　on　a　wide　range　of　substrates　forms　the　basis　for　large-area　applications,　such　as　graphene　integration　with　silicon-based　technologies,　which　requires　graphene　on　silicon　with　outperforming　carrier　mobilities.　However,　2D　materials　were　only　produced　on　limited　archetypal　substrates　by　chemical　vapor　deposition　approaches.　Reliable　after-growth　transfer　techniques,　that　do　not　produce　cracks,　contamination,　and　wrinkles,　are　critical　for　layering　2D　materials　onto　arbitrary　substrates.　Here　we　show　that,　by　incorporating　oxhydryl　groups-containing　volatile　molecules,　the　supporting　films　can　be　deformed　under　heat　to　achieve　a　controllable　conformal　contact,　enabling　the　large-area　transfer　of　2D　films　without　cracks,　contamination,　and　wrinkles.　The　resulting　conformity　with　enhanced　adhesion　facilitates　the　direct　delamination　of　supporting　films　from　graphene,　providing　ultraclean　surfaces　and　carrier　mobilities　up　to　1,420,000　cm(2)　V-1　s(-1)　at　4　K.