You have to assume, for the sake of sanity, that they don't need to be built in the system you want to collapse. The thought of needing a colony with the resources to build one in 12 different systems is terrifying. The fact that the "ship" stats look like orbital stats is confusing, though.

I think they are almost certainly "used up" after a number of uses defined by your level of Graviton Physics. That would be the only way to justify the fact that it costs so little compared to the Planet Killer when the effects (in terms of win condition) are so similar. And if you accept that they have multiple uses, then they must be mobile, right?