Hexagonal crystals are suitable underlayer candidates for hexagonal boron nitride (h-BN) heteroepitaxy due to their similar in-plane atomic arrangement. When the thickness of h-BN is beyond a critical value, its accumulated stress resulting from the lattice mismatch can be relaxed by generating dislocation or changing into three-dimensional growth. Here we calculate the evolution of h-BN critical thickness with the growth temperature when it is grown on various frequently-used hexagonal crystals for both cases. The results show that in order to minimize the lattice mismatch, a low growth temperature is preferred when grown on GaN or Si(111) while on the contrary when grown on 6H-SiC or alpha-Al2O3. Besides, AlN is the most unique underlayer as its lattice mismatch with h-BN is relatively small (< 0.7%) and they can even fully match around 1150 K, which means it can be used as a buffer layer for thick h-BN (> 100 nm) growth. Moreover, large area of two-dimensional thin h-BN (5-15 nm) layer can be obtained on GaN, 6H-SiC, Si(111) or a-Al2O3 except for graphene. On the other hand, calculation indicates that large area of graphene can be grown on h-BN. (C) 2017 Published by Elsevier B.V.