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Molecular dynamics is used in combination with density functional theory to determine the thermal transport properties of the single-layer hexagonal boron nitride (SL h-BN) from ab initio calculations. Within this approach, the possible anisotropy in the thermal conductivity of SL h-BN was studied. For samples with finite length (of the order of 20 nm), we find a significant dependence of the conductivity on the transport direction. We make a direct comparison of the results obtained for two-dimensional (2D) layers and for nanoribbons with similar size, and show that, as a consequence of edge scattering, the ribbon geometry induces a significant decrease in the conductivity, and produces a strong change in the anisotropy. For the zigzag and armchair transport directions, the dependence of the thermal conductivity on the system length was also obtained, as well as its value in the 2D bulk limit case. A very small anisotropy was found for the limit of long samples, in contrast with the finite length ones. This is explained analyzing the dependence of the average square group velocities on the transport direction and the phonon frequency

Thermal and transport properties of pristine single-layer hexagonal boron nitride: A first principles investigation