If Disney acquires Fox, they could potentially own a part of Batman's TV history. The Walt Disney Company has been floating the idea of acquiring 21st Century Fox's movie and TV divisions, namely 20th Century Fox, for some time now. So far, the primary focus has been on the Mouse House (and, in turn, Marvel Studios) gaining the film rights to the X-Men and the Fantastic Four, thus allowing both teams to inevitably join the long-running Marvel Cinematic Universe, but there's much more to this deal than meets the eye.
If Walt Disney Studios does acquire 20th Century Fox, the deal will bring about many questions regarding Hollywood's future, as well as what will become of Fox's major properties, such as Alien, Avatar, and The Simpsons, and even the studio's platforms, such as FX Network and Fox Searchlight (a pioneer in major indie films). But the thing is, The Simpsons isn't the only age-old TV show that will come under Disney's control, should the deal go through. If the Mouse House does, indeed, buyout Fox, a part of Batman's history may soon be under the control the Marvel-owned studio.
CBR notes that 20th Century Fox Television still holds the rights to the original 1966 Batman TV series, famously starring Adam West as the Caped Crusader and Burt Ward as his trusty companion, Robin. The network produced and distributed the series in the '60s and retains the rights to the TV show despite Warner Bros. retaining full ownership of DC Entertainment today, just as 20th Century Fox continues to own the rights to George Lucas' original Star Wars film even though Disney acquired Lucasfilm in 2012.
Before Warner Communications (later Time Warner) bought DC Comics (later DC Entertainment), National Periodical Publications owned the comic book publisher and they sold Batman's TV rights to ABC for $7,000 in the early '60s, which the network later awarded to 20th Television, who developed the 1966 Batman TV series for ABC. Although Fox controls the program, the series' rights have been stretched between Fox, Warner, and the Greenway Productions (who recently sold their remaining ownership in Batman to Fox), with all parties dependent on one another to produce any new content or merchandise regarding the series. If Fox is bought out by Disney, the rights to the 1966 Batman TV series may transfer to the Mouse House along with the X-Men and Fantastic Four film rights.
What's interesting is that FOX Broadcasting is now airing another Batman-related TV show over 50 years later: Gotham. Unlike the 1966 Batman TV series, though, Gotham is fully produced, distributed, and owned by Warner Bros. Television, thus allowing them to move the show over to another network should a Disney-owned Fox (if Disney also acquires FOX Broadcasting) decide to cancel the program.