Frank Zappa’s rich musical and cultural legacy, and which children have a right to profit off it, have recently become the subject of a public and contentious family battle.

The children of Frank and Gail Zappa – Moon Unit, Dweezil, Ahmet and Diva – were left unequal shares of the Zappa Family Trust, which owns the rights to a massive trove of music and other creative output by the songwriter, filmmaker and producer — more than 60 albums were released during Zappa’s lifetime and 40 posthumously.

Thanks to a decision by their mother, who died in 2015, Ahmet, 42, and his younger sister, Diva, 36, share control of the trust — to the dismay and anger of their two older siblings, Dweezil, 46, and Moon, 48, who received smaller portions.

But each inherited equal levels of their father’s independent spirit, a sensibility that is seeing renewed attention due to the arrival of the documentary “Eat That Question: Frank Zappa in His Own Words.”

Below is a look at what the Zappa kids are up to now.

Moon Unit Zappa

Moon Unit Zappa (Carolyn Cole / Los Angeles Times)

The eldest Zappa child is arguably the most well-known, due in large part to her teenage star turn on “Valley Girl.” The song, a collaboration between father and daughter that appeared on Frank’s 1982 album “Ship Arriving Too Late to Save a Drowning Witch,” poked fun at the California Valleyspeak dialect unique to teenage girls in the San Fernando Valley at the time.

In the intervening decades, Moon has continued to live a creative life, appearing on such TV series as “Curb Your Enthusiasm,” “Grey’s Anatomy” and “How I Met Your Mother.” More recently, she voiced a character on the Fox’s animated show “High School USA!” Moon writes for film and television, does stand-up comedy and recently held a storytelling show in Portland, Ore. The artist is also very involved in yoga.

During a recent conversation, Moon (who considers “Unit” to be her middle name) said that she had wanted to help spread the word about her father’s work and legacy but that Gail had mostly declined her ideas. She noted this was not a family fight over money or unfair proportions, recently tweeting, “This is about having to ask permission for use on OUR last name & creative exclusion.”

“There were so many times that I had gone to her. I had suggested a biopic and a documentary. I had lined up all these elements,” said Moon, adding that she also pitched a family reality show and a curated album of Frank’s music designed with teenage girls in mind. “Every single idea I brought to her, she shot down.”

Moon said she loved “Eat That Question,” the new documentary about her father, calling it “such a universal story about following your calling, and how that road is not an easy road. It requires a kind of stamina and dedication, and that’s a great story, whether you’re a fan of that music or not.”

At the top of Moon’s creative to-do list is a project sure to excite fans of Zappa and Los Angeles culture: “I'm working on a book about growing up in my crazy house.”

Don’t expect her to pull any punches.

Dweezil Zappa

Dweezil Zappa (Francine Orr/ Los Angeles Times)

The oldest son, perhaps best known to the public as an MTV VJ in the 1980s, is the most musically focused of the four kids. It’s Dweezil’s beef with the trust that first drew press attention to the behind-the-scenes drama surrounding use of the Zappa name.

Specifically, the trust is trying to prevent Dweezil from touring as either Zappa Plays Zappa or Dweezil Zappa Plays Frank Zappa, citing trademark violations.

Until the tussle is settled, Dweezil will be touring under his own name, and he has dubbed that sojourn the Cease and Desist tour. He and his band will be performing his father’s work, with particular attention paid to songs from the Mothers of Invention’s “Freak Out!,” which this week celebrated its 50th anniversary.

I, of all the people in the family, spent time with him doing something because we had it in common -- guitar [and] music. — Dweezil Zappa said of his father

Dweezil takes his job as Frank’s musical ambassador seriously. “My concern is to just be able to continue to enjoy the music, live within the music, play the music, and express that and allow new people to discover that in a live situation,” he said.

“I, of all the people in the family, spent time with him doing something because we had it in common -- guitar [and] music.”

In addition to playing his father’s music, the skilled guitarist has landed guest appearances over the years with such artists as Winger, Pat Boone, Spinal Tap (lead guitar on “Break Like the Wind”), Weird Al Yankovic and the Dixie Dregs.

Last year, Dweezil released his first solo album in nine years, “Via Zammata,” featuring work that mixes rock, jazz and funk. The album’s highlights include the mesmerizing instrumental “Truth,” the jangly, Beatles-esque pop of “Just the Way She Is” and a Zappa-inspired experiment called “ Malkovich ,” which features vocals by John Malkovich.

Dweezil Zappa begins his Cease and Desist tour in El Prado, N.M., on July 1.

Ahmet Zappa

Ahmet Zappa (Robert Gauthier / Los Angeles Times)

Ahmet has taken charge of day-to-day operations of the Zappa Family Trust. Although those responsibilities are myriad and include running its record labels, advancing Frank’s legacy and protecting his copyrights, Ahmet views his main role as serving the will of the fans and “for people to make the connection to my father's entire body of work.”

Running the trust is “totally in my wheelhouse,” he said during a recent conversation at the Zappa compound. In his professional career, he’s run a division of Disney called Kingdom Comics and, with his wife, Shana Muldoon Zappa, created the Disney-owned brand Star Darlings, which is centered on empowering tween girls. Star Darlings merchandise includes books and dolls and is available at Wal-Mart, Target and other big-box stores.

What's great about Frank is that he really is the person guiding things, because he said it, he played it, he shot it. He really is the moral compass. — Ahmet Zappa

Said Ahmet, “I always wanted to be a storyteller. That makes me the happiest – storytelling in any medium.”

He added that when it comes to his philosophy on matters of the trust, he need only refer to his father’s blueprint. “What's great about Frank is that he really is the person guiding things, because he said it, he played it, he shot it. He really is the moral compass.”

Describing his father as “a complicated person” and an amazing musician, Ahmet said that one of his jobs as trustee was to convey the sheer breadth of Frank’s compositional skills. “One thing that I want people to understand, which I think is underdeveloped, is the focus of him as a modern-day composer. His orchestral pieces, that aspect of his life -- more and more people want to play that music, which makes me so happy.”

Ahmet added that while his dad provided posthumous guidance, he learned how to run the business by looking to his mom. Citing “what my mother endured, and her business mind, and her creativity,” he said, “It's pretty cool to be more like Gail Zappa.”

Diva Zappa

Diva Zappa (Twitter)

The youngest Zappa child is also the most press-shy.

Speaking on the phone from London earlier in the month, Diva had just returned from Prague, where the Czech National Symphony Orchestra had performed an evening of her father’s music. She said that one of her primary roles in the trust is to be present when her father's work is highlighted.

“What do I think my responsibility is? To show up and be open,” she said. “Experience everything. Show up and see what happens and try to do the best I can in every situation for the good of everyone in my family. And that’s including future generations. Everything we do is really to take care of all of us.”

Aside from her role in ensuring Frank’s legacy, Diva is a visual artist and fashion designer who works with knitwear.

"When I knit, I never know what will happen,” Diva told the British newspaper the Independent in 2011. “I am inspired by all that is around me, light, trees, leaves, colours, breath, sounds, sparks, magic, beauty, frustration, heat, love, coffee, humour, feathers, shadows, smells... everything. It all gets in there somehow."

The designer’s work appeared on the Grammy red carpet in 2009 when Metallica bassist Robert Trujillo’s wife, Chloe, wore a Diva dress.

Diva is currently at work on a scarf, but not just any scarf. “Emilio the Scarf” is a project with its own Twitter handle. Described on the profile page as “a magical piece of art,” the scarf promises that “one day I will be 5,280 feet long.”

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UPDATES:

9:13 a.m., July 1: This story was updated with a recent tweet from Moon Unit Zappa.

This story was originally published at 3:46 p.m. on June 30.