The effect of humidity on intercalated water between exfoliated graphene and mica has been previously reported. At low humidity, epitaxial one-layer thick icefractals form. The growth of the icefractal is initiated by the heat extracted from the system by evaporation, into the 3D ambient, of the second layer of water intercalated between mica and graphene under low humidity conditions. Here, we study the fractal shape dependence on the graphene cover and the evaporation rate of the water molecules from the double bilayer. We found that the thickness of the fractals' fingers scale as the square root of the ratio of the bending energy of graphene plus the surface energy of the intercalated ice and the product of the velocity of the fractal front and a term related to hindrance of the water ad-molecules. Icefractals formed under a thick graphene cover and upon a low evaporation rate are thick with few side branches, whereas fractalsgrown upon high growth rate under single-layer graphene are thin and very ramified. We attribute the coarsening of fractals to the extra degree of freedom of the surrounding water molecules, enabled by the non-complete adaptation of the ice crystal's morphology by the graphene cover.