Olivia Wilde, Jason Sudeikis Fighting Over Child Support Issues

Olivia Wilde and Jason Sudeikis may have been hugging recently, but not because they've resolved their conflicts -- TMZ's learned there's a dogfight over how child support will be handled.

Sources with direct knowledge tell TMZ ... Jason's New York lawyer, Bill Beslow, has gone to a New York judge to resolve all child support issues. The reason it's sticky is that last July both a New York judge and a California judge ruled all CUSTODY issues should be handled in L.A.

We've learned Beslow went to a New York court January 4 and asked the judge to handle all child SUPPORT issues, and the judge set a hearing date for February 15.

Sources connected to Jason say he does not want any child support from Olivia. We're told he's willing to pay her "a reasonable amount" in child support either decided by the 2 of them or a New York judge.

Our sources say Olivia is baffled because both a New York judge and a California judge have already said this is an L.A. and not a New York case. She wants both custody and child support decided in L.A.

Beslow is appealing the decision to have custody decided in L.A. As for Olivia, we know her lawyer, Laura Wasser, and Olivia's New York lawyer have filed legal docs asking the judge on February 15 to dismiss Beslow's move to handle child support in New York, so a judge in L.A. can decide all issues involving the children.

Short story ... this dispute is far from resolved.

As for Olivia and Jason hugging a few days ago ... we are told very clearly -- they are NOT getting back together.