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Focusing towards ternary metal hydrides has recently been regarded as a new avenue for research in pressure-dependent high-temperature superconductors, thanks highly to a fairly large number of permutations of alloying metals, even metalloids, with hydrogen. Herein, new phases of Mg- B- H ternary hydrides are predicted from the first-principles evolutionary techniques, as a result of which the corresponding phonon and electronic calculations for the three candidate phases are performed successively to confirm their dynamic stability and the possibility to become conductors. The metallic MgBH9 undergoes a superconducting phase with a maximum Tc of 64 K at 110 GPa, with its spectral function predominantly active around optical modes. The significant increase in cumulative electron-phonon coupling constant is associated with a relatively low cutoff frequency according to the bandwidth function. As for the non-metallic candidate, hydrogen-vacancy diffusion kinetics of the MgB2H8 phase are determined by means of total energy calcula- tions. Stable pathways at varying pressure are reported, suggesting that elevated pressure lowers the activation energy which is presumably due to an optimal level of average nearest H- H(B) inter-fragment distances.