New Line will be responsible for handling films based on the Vertigo imprint of DC Comics going forward, while DC Comics superhero films will remain the purview of Warner Bros., according to Deadline.
According to the report, Warner Bros. currently has its hands full with a full sleight of DC Comics superhero movies, including Batman v. Superman: Dawn of Justice, Suicide Squad and Aquaman. As such, they've decided to hand off responsibilities for the comparatively subversive Vertigo properties to sister studio New Line.
The most likely candidate for film New Line Vertigo film out the gate would be The Sandman, which Joseph Gordon-Levitt is already set to direct and star in. Other properties under the Vertigo film banner include any potential future film plans for Constantine, Justice League Dark/Dark Universe, Preacher and Lucifer.
EDIT: While confirming the general report, THR's Borys Kit claims that the Justice League: Dark Universe characters, including Swamp Thing and Constantine, will remain with Warner Bros. We're also uncertain about Preacher, as AMC is readying a TV adaptation of the series for the fall.
Also: Justice League: Dark Universe, which has heroes like Swamp Thing and Constantine, and were once Vertigo titles, remain at big Warners.— Borys Kit (@Borys_Kit) June 29, 2015
Which other Vertigo Comics properties are under New Line remains hard to judge, given the shared ownership contract with many of those comics' creators.