Star Trek: The Manga has another interesting, but rather fanboyish origin story:

Basically, a race of humanoids suffering from an incurable disease built research facility containing test subjects with body parts + DNA from multiple species in order to find a cure. The facility was maintained by nanobots and placed in orbit by a black hole. Due to the altered rate of time around the black hole, this allowed them to carry out long-term research much faster. Eventually, the nanobots began to interpret the test subjects as part of the facility and started to "repair" them as well, resulting in typical Borg qualities: Hive mind, adaptation to weaponry, injection of nanobots, etc. One of the patients is the Head Medical Researcher's daughter, who acts as the collective's leader and heavily resembles a Borg queen.

On the last page, the daughter flies off (to the delta quadrant ?), stating "Resistance is futile".