After the discovery of Graphene in 2004, the research based on possible findings of other 2D structures are at peak due to the absence of band gap in graphene. Among the new generation 2D materials, TMDs are one of the rising stars due to its wide variety of electrical and mechanical properties in between the semiconductor and metal. Moreover, the bilayers of 2D materials are receiving more limelight due to its unique properties such as layer-dependent tunable optoelectronic and mechanical behavior. These bilayers are attached to each other by weak van der Waals force and the control over the experimental growth technique is required in order to synthesize deserved stacked products. Among several existing growth techniques, epitaxial growth mechanism is the most preferred one due to its technological advantages such as reduction of defect density (e.g., tilt grain boundaries), consistency in the overall growth, final products with sharper interfaces. Computational analysis involving Density Functional Theory (DFT) and Molecular Dynamics (MD) simulation is necessary to gain deeper insight into the post-growth analysis. We, therefore, considered different bilayers such as, WS2-WS2, WS2-WSe2, MoS2-MoS2, and MoS2-Graphene and compared their properties (electronic and physical). We considered both the chalcogen and metal terminated edge as the initial TMD structure to grow and we have also considered the length effect and the orientation effect of the second layer towards the formation energy of the overall structure. We find that the growth temperature plays a crucial role in governing the growth mechanism. The difference of formation energies of different TMD leads to the reaction rate difference and the growth temperature of TMD layers. For example, we find that formation energies of MoS2 and WS2 are 2.48 and 2.70 eV respectively and hence growth temperature of the WS2 (~ 800-1050) are higher than MoS2 (~ 600-850). At the controlled growth temperature, for chalcogen termination, one-step growth mechanism is preferable where the second layer starts from the center (core) and grows outwards (edge). On the contrary, for the metal terminated edge, two-step growth is preferred where the second layer starts from the edge and grows inwards (core). Our results conclude that the evolution of various TMD homo/hetero-structures originates from the competition between the adsorption, desorption, and the diffusion of metal (Mo, W) and chalcogen (S, Se) atoms under various growth temperatures. Our computational work provides a more in-depth understanding and guidelines of design and fabrication of TMD heterostructures.