A judge yesterday began untangling the legal web surrounding Broadway director Julie Taymor’s claim that she’s owed millions in royalties for “Spider-Man: Turn Off the Dark.”

Taymor says the 2 1/2-page treatment she wrote for “Spider-Man” in 2004 — and which was approved by the show’s producers, who include Bono and the Edge — entitles her to royalties because it remains the basis for the show.

Taymor was booted from the $75 million production in March 2011 after critics blasted the show — and after a string of serious injuries to cast members performing elaborate stunts.

Taymor lawyer Charles Spada argued that she deserves a bigger cut of the show’s proceeds because it still incorporates her ideas — including a new character, Arachne, who is never mentioned in the Spider-Man comics.

“There is originality,” Spada said.

In court papers, Taymor also claims that the book “theatricalizes in novel ways the familiar story of Peter Parker and his love interest Mary Jane Watson.”

But “Spider-Man’s” producers argue that Taymor doesn’t deserve more money, partly because in its current form the show is very different from the version she helped create.

“The whole darn thing came from the comics,” said Dale Cendali, a lawyer for the producers.

“What they’re trying to do is put a lien on the ‘Spider-Man’ property,” Cendali said. “They can’t monopolize Spider-Man. They don’t own Spider-Man.”