Is Johnny Depp still with Vanessa Paradis or seeing Amber Heard?

 Among the more complicated celebrity relationships may be the one involving Johnny Depp and longtime love Vanessa Paradis.

In the wake of reports the “Dark Shadows” star and the French singer had split after 14 years and two children, the couple put out the word they are not kaput, even though they have not been seen together in public for more than a year.

There were indications that a fling between Depp and his “The Rum Diary” co-star
Amber Heard may have led Paradis to pull the plug, but that was denied by them, even as “Diary” insiders claim it was true.Making it all even more complicated: Heard recently admitted she is bisexual and is involved with artist and photographer

Tasya van Ree.

Yet, there also have been recent sightings of Heard and Depp — though the privacy-obsessed Depp has been able to avoid being photographed with Heard, at least so far.

NEW DIRECTIONS: After making three films in Europe, Woody Allen returns stateside this summer, filming with Cate Blanchett, Alec Baldwin and comedian Louis C.K. in New York and San Francisco, where he made his directorial debut with “Take the Money and Run” in 1969. … I’m hearing Dem biggies are telling President Obama to avoid too many future celeb-centric fund-raisers like the one next week hosted by Sarah Jessica Parker. “That ‘Mr. Hollywood’ label only gives the Republicans ammunition to attack him as a limousine liberal,” said a longtime Obama supporter.

BOOK BEAT: Financial guru Mellody Hobson hosted a group of pals Monday to toast ex-ABC News prez David Westin’s new Exit Strategy book — highlighting his decade-long run at ABC, shepherding such unforgettable stories as the death of Princess Diana, the “tied” 2000 presidential election and 9/11. Among those on hand for the Arts Club fete were Margot Pritzker, Bill Bartholomay, Peter Bynoe, Linda Johnson Rice and news pros Cheryl Burton, Linda Yu and Dorothy Tucker.

† For his annual “Early Birds & Bookworms” breakfast at RL — supporting the Jane Addams Senior Caucus — Bunky Cushing brought in New York socialite, animal activist and author Cornelia Guest, who charmed the SRO group of Chicago’s Very Visibles on Tuesday while boosting her Simple Pleasures book about “cruelty free” vegan cooking and entertaining. When the lifelong vegetarian and animal lover listed a number of her pets over the years, a mention of “my donkey Madonna” brought a few chuckles. “Duly noted she didn’t call her an ass,” quipped one wag.

STAR POWER: As usual, Jeremy Piven will be back home June 23 to attend the annual fund-raiser for his family’s Piven Theatre Workshop — joined at the Noyes Cultural Center event in Evanston by the Bears’ Charles Tillman and Lance Briggs.

† Speaking of Tillman, the NFL pro hosts his “Celebrity Pro BOWLer Tournament” Thursday at the Kings Lanes Lounge & Sports — joined by a big bunch of supportive teammates raising funds for kids’ health issues.

CORRECTION: While filmmaker Alexander Payne will be in Chicago on both June 16 and 23 (as reported here yesterday), his participation in the kickoff of the Greek Film Fest happens June 23.

Bill Zwecker reports on “Good Day Chicago” and “Fox Chicago News at 9” on WFLD-Channel 32.