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In this work, we present a comparative first principles study of mechanical properties, electronic structure, phonon dispersion relation, electron-phonon coupling and magnetism in three isostructural superconductors, namely, ThFeAsN, ThCoAsN and ThNiAsN. Experimentally, ThFeAsN and ThNiAsN show superconducting properties, while ThCoAsN has not been synthesized. Our calculated elastic constants show that all these systems are mechanically stable. Significant differences in the electronic structures of these three compounds in terms of density of states, band structures and Fermi surfaces, are found. Our phonon calculations reveal that all the systems including ThCoAsN, are dynamically stable. Phonon dispersion relations indicate that the optical modes of all the three systems are almost the same while there are significant variations in the low frequency manifold consisting of mixed modes. The electron-phonon coupling constants and superconducting transition temperatures calculated based on the Eliashberg formalism, predict a rather high $T_c$ of 6.4 K for ThCoAsN and also a $T_c$ of 3.4 K for ThNiAsN which agrees well with the experimental value of 4.3 K. Nevertheless, we find a $T_c$ of 0.05 K for ThFeAsN, which is much smaller than the experimental $T_c$ of $\sim$30 K. However, a simple analysis considering the amplifying effects of spin density wave order and out-of-plane soft phonon modes suggests that the $T_c$ could be increased considerably to $\sim$10 K. Finally, we also discuss the effect of anion As height on the electronic structures and study possible magnetic states in these three compounds.