2D in-plane and vertical heterostructures such as graphene and hexagonal boron nitride (h-BN) have drawn wide attention owing to their unique structure and properties over the past years. [1][2][3][4][5][6] Previous studies have explored their controlled growth, detailed interface microstructure, properties, and device applications. [7] For example, the interface of in-plane or vertical heterostructures can be controlled to be atomically sharp or clean at a proper growth condition, and the intriguing properties such as half-metallicity, [8] magnetism, [9] or peculiar boundary states [3,10] have been theoretically predicted or partly confirmed by experiments. On the other hand, the in-plane heterostructure system is also an ideal system for deeply studying related epitaxy behavior and kinetic process beyond conventional A-A or A-B material systems. For example, grapheneh-BN system provides a rich possibility of epitaxial templates with various dimensionalities and interface, such as 2D crystal surfaces, 1D edges, inner 1D grain boundaries (GBs), and 1D interface of graphene-h-BN. Among these possibilities, 1D graphene zigzag (ZZ) edges were previously studied in depth for the epitaxial growth of h-BN. [11,12] While h-BN growth along other various graphene edges fabricated by top-down etching was also demonstrated, graphene edge configurations are essentially unknown. [13,14] However, much less is known about the related kinetic growth of complex epitaxial systems. To date, it is not clear whether the growth of 2D materials on templates of various dimensionalities is allowed in practice, and no effective idea or model is available for describing the complex epitaxial growth kinetics.Here, using a 2D A-B (A: graphene and B: h-BN) system with the freedom of in-and out-of-plane epitaxial growth, we discover a set of new epitaxial growth patterns, spanning from edge-configuration-dependent growth along 1D graphene ZZ to armchair (AC) edges, GB formation by merging materials, 1D GB-or A-B interface-templated growth of adlayer, to adlayer growth on 2D surface template. We further provide, for the first time, a framework that allows the description of various kinetic growths of epitaxial structures by combined geometric and structural modeling. This work provides a general viewpoint for understanding epitaxial growth in complex systems.We started the growth of single crystal hexagonal graphene flakes (HGFs) with desired sizes and densities on liquid Cu surface by modulating experimental parameters such as methane, H 2 , and Ar flow rates. [15] The formed regular monolayer HGFs Epitaxy traditionally refers to the growth of a crystalline adlayer on a crystalline surface, and has been demonstrated in several simple material systems over decades. Beyond this, it is not clear whether the growth of 2D materials on templates of various dimensionalities is possible, and no effective theory or model is available for describing the complex epitaxial growth kinetics. Here a library of hexagonal boron nitride epitaxy is presented on ...