With the advanced technology of the Borg - one is all thats needed.
In DS9 Rom made self replicating mines and in First Contact with limited supplies the Borg assimilated a lot of the crew and ship. Logically the only way this could be done is with self replicating technology - almost as organic as the human (Klingon, Vulcan, whatever...) parts that remain.
If Rom (granted, he was seem as an an idiot savant, but still an idiot) could come up with the technology, surely the Borg with all their assimilated and self-discovered knowledge could do the same. First Contact and Sevens never ending supply, to me anyway, says to me that they are self replicating. There may have been something on-screen about this, but I can't remember it... sadly I've probably forgotten more than I know...
But if one nano probe could self replicate and make two, then that two made four... you'd have Tribble like multiplication. The more you give a victim, the faster they change.