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Personally, I think it makes no sense that any given commander leaves their vessel to commandeer the battlecruiser. It leaves the given ship vulnerable to being disconnected from its commander. And it leaves too much possible animosity between the commanders from the prestige gain of the singular prize crew captain.
What I imagine will likely be the most rational option. Is that the ONI black box Xenotech specialists on our ship transfer over and commandeer the vessel. It would make much more sense to me that they would be the ones who would take over the operation as a third-party organization.