In Star Trek:First Contact, entire decks are "assimilated" with Borg technology within a matter of hours.
Do Borg structures, such as alcoves, "grow" by themselves (kind of like implants), or are they manually built by drones?
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I think First Contact was produced and released before the first Voyager episode (the only assimilation we saw in TNG was when Picard was captured in The Best of Both Worlds), but Voyager fleshed out a lot of the Borg assimilation process and technology that First Contact hinted at.
Borg technology is nanite based - that is why we see them inject something into the crewmen in First Contact. Just nanites are able to biologically assimilate people, it can be assumed that other nanites are reconfiguring the ship and environment to assimilate the technology.