5:00 PM PT -- A source close to Jason tells TMZ ... "Papers were drawn up to establish jurisdiction relating to the children of Ms. Wilde and Mr. Sudeikis."
The source adds ... "Mr. Sudeikis had no prior knowledge of the time or place that the envelope would have been delivered as this would solely be up to the process service company involved and he would never condone her being served in such an inappropriate manner."
Olivia Wilde endured a bit of embarrassment at CinemaCon this week -- while she was in the middle of screening the trailer of her new movie -- her ex served her legal docs.
The awkward moment was seen by multiple people who were in the room Tuesday when OW was on hand in Vegas to screen a never-before-seen trailer for her erotic thriller flick "Don't Worry Darling" -- which stars her beau Harry Styles and Florence Pugh.
The word is ... while Olivia was talking on stage, somebody came up and placed a manila envelope right down next to her at her feet -- which was marked 'Personal and Confidential.'
Olivia was photographed picking it up, taking a peek inside ... and then carrying on like nothing had really happened. But something certainly had -- according to Deadline, there were court papers in there courtesy of Jason Sudeikis ... with whom she shares two children.
The outlet says, citing sources, the docs involve child custody. As you know, they publicly split about a year and some change ago ... and since then, she's been in a whirlwind romance with Harry -- whom she also cast in her highly-anticipated film.
It appears that Jason and Olivia were getting along okay in the wake of their split -- but this clearly suggests otherwise. You gotta figure Jason wouldn't just do this to embarrass her if he didn't have to ... so, presumably, he hadn't been able to get these to her in a normal setting.