Methods of forming a graphene material on a surface are presented. A metal material is disposed on a material substrate or material layer and is infused with carbon, for example, by exposing the metal to a carbon-containing vapor. The carbon-containing metal material is annealed to cause graphene to precipitate onto the bottom of the metal material to form a graphene layer between the metal material and the material substrate/material layer and also onto the top and/or sides of the metal material. Graphene material is removed from the top and sides of the metal material and then the metal material is removed, leaving only the graphene layer that was formed on the bottom of the metal material. In some cases graphene material that formed on one or more side of the sides of the metal material is not removed so that a vertical graphene material layer is formed.