While Doctor Who and Star Trek built two of the biggest sci-fi universes in pop culture, the vast worlds of these franchises stayed apart for decades. But in 2012, the worlds of the Eleventh Doctor and Star Trek: The Next Generation collided in the series Star Trek: The Next Generation/Doctor Who: Assimilation² by Scott Tipton, Dovid Tipton, Tony Lee, J. K. Woodward and the Sharp Brothers. The series saw the crews of the TARDIS and the Enterprise face off against two very similar cybernetic races, one from each other's universes, the Cybermen and the Borg.
When the planet of Delta IV is attacked, the citizens find themselves converted into both Borg and Cybermen. Meanwhile, the TARDIS crew, which at this time consists of the Eleventh Doctor, Amy and Rory, materializes in what they think is 1940s San Franciso but, in reality, is the Holodeck of Captain Jean-Luc Picard's Enterprise.
The crew of the Enterprise initially mistakes the time travelers for rogue computer elements but are shocked to discover their true nature. The Doctor is next to be shocked when he realizes he knows what a Klingon is -- because he knows he shouldn't. Captain Picard is skeptical of the strangers, however his concerns are eased by Deanna Troi who senses no ill intent from them. However, these introductions are interrupted when they get the news of Delta IV and both the Doctor and Picard recognize their respective adversaries.
The similar ideologies of the Borg and the Cybermen, their belief that all life should be united under a single collective cybernetic existence, has reached an unnerving alliance. This is made clear by the image of their leader, a Cyber Controller fitted with Borg technology.
As the Enterprise crew search for any information on the Cybermen, the Doctor experiences a memory he shouldn't have. The art style changes as the focus switch to the adventures of James T. Kirk and the original Enterprise. They meet the Fourth Doctor, as played by Tom Baker, and encounter the 1970s-style Cybermen. The Eleventh Doctor remembers this adventure but also remembers not remembering it.
When Picard takes the Doctor to meet Guinan, the two recognize each other, although both know they shouldn't. Picard seems confused but they explain how they are both time-sensitive beings, meaning they can sense that elements of this universe are being altered by elements of the Doctor's and the imminent danger that presents.
An expedition to Cogen V reveals the Cybermen have betrayed the Borg. The Borg soon contact the Enterprise to ask for Picard's help. After Guinan explains Picard's resistance as a reaction to his assimilation, the Doctor shows Picard what happens if he doesn't help the Borg -- a universe conquered by the Cybermen.
Picard agrees to meet the Borg, led by Conduit (a close friend of Riker's who has been assimilated.) They explain how the tensions between their similar beliefs, which came to a head when the Doctor arrived, came to a point where neither saw each other as compatible anymore. The Doctor helps the Enterprise crew secure gold, the Cybermen's weakness, leaving only one thing left to obtain -- a copy of the Borg's executive library. The Doctor and friends travel to the Battle of Wolf 359 and obtain a copy, and see for themselves how the Borg turned Picard into Locutus.
The Doctor, Amy and Rory, along with an Enterprise strike force, take the TARDIS to the heart of the Cybermen fleet before they can fully convert the Borg Homeworld. Worf's team manages to disable the engines, allowing the Enterprise to catch up and disable the Cybermen with a gold-infused particle beam.
Conduit tries to assimilate the TARDIS, but the heart of the TARDIS retreats into Data and immobilizes Conduit. Worf and Rory throw Conduit into the time vortex, ending their troubles with assimilation. After the smoke from their adventures clears, the Doctor, Amy and Rory leave the Enterprise, returning to their own universe.
Whilst the series showed how similar the Cybermen and Borg were, it made clear that two races both dedicated to faceless assimilation will still disagree on how that assimilation should play out. Both the Enterprise and the Doctor put an emphasis on exploring strange new worlds, Picard's stance in the crossover also highlighted the military leanings of Starfleet, which contrast sharply to the Doctor's philosophy. Still, this crossover ultimately underscores how similar these two universes are by putting some of the most beloved incarnations of their characters together for the first time.