Delug became one of MOCA’s trustees in 2004. But when the board, despite what she considered the dismaying restrictions attached, accepted collector Eli Broad’s offer last winter of $15 million in matching funds to help the institution out of its financial distress, she tendered her resignation, along with Jennifer Simchowitz and Ruth Bloom. "There are many ways I can support MOCA without having the word trustee next to my name," says Delug. This past May, for example, she and Simchowitz cochaired MOCA’s biannual auction, which raised $650,000 for the museum.

MOCA does not claim her undivided attention, however. In 2004, Delug also joined the Hammer Museum’s board, motivated in part by her friendship with Hammer director Ann Philbin, and has earned kudos there for her willingness to underwrite exhibitions and acquisitions at a time when many are cutting back. "I am equally involved with both institutions," Delug says. "You can have more than one child and love them both." That affection extends to the curators and directors, of whom she says, "These people became my friends and teachers."

Indeed it was Schimmel who encouraged one of her most significant purchases: a spectacular Bruce Nauman drawing of the words "Death Life Love Pleasure Pain" arranged in a multicolored circle. He spotted it three years ago at the Art Basel Miami Beach booth of the New York dealer Christophe Van de Weghe. "I said, ‘Rosette, you’ve got to look at this,’" Schimmel recalls, adding that at $650,000, it was "a price point she had never jumped to. [But] she understood that when it was in her house, it would make her a better collector." For Delug, the acquisition represented a willingness to embrace Conceptual work. "To spend that kind of money on a few words on a piece of paper," she says, "it really had to be art."

The Nauman holds pride of place in the collection that Delug has displayed throughout the midcentury house she bought three years ago. Situated atop the hills of the exclusive Trousdale Estates, it encompasses 8,000 square feet of mostly open space, with vast windows revealing what realtors call "jetliner" views of Los Angeles. On a recent afternoon, wearing a black T-shirt and pants, with dozens of thin gold bracelets encircling her bare forearm, Delug is moving some pieces around the house. Leaning against a wall is a digital collage by the duo Simmons & Burke that she bought last fall from their first show at L.A.’s Kim Light/Lightbox gallery and needs to make space for.

"The first few years, Rosette accumulated," says Gordon VeneKlasen, director of the Michael Werner gallery in New York. "Now she is concentrating on what she really likes." Delug has begun to pursue more European artists. She bought a Sigmar Polke self-portrait photograph at a fair a few years ago, and since then VeneKlasen has sold her two other works by the artist: an amber painting and a mixed-media piece featuring enlarged newspaper photos of a nude man and woman. Delug explains that her interest in Polke and other more-established artists has come from talking with younger artists she admires and collects: "I heard about who they respected, and I started looking into them. It’s a normal graduation."

In displaying her collection, Delug has created a rambunctious dialogue between established artists and newcomers. Hanging on a living-room wall is a riff on traditional British portraiture by Richard Wathen that she purchased from Max Wigram, in London, while a Jim Lambie sculpture made of colored folded doors tumbles across the floor. In the foyer an expansive abstract work by the up-and-coming painter Tomory Dodge faces simple graphic works by such major names as James Lee Byars and Lee Bontecou. A delicate chain sculpture by Liz Larner is draped over a chest near a sitting room. The great room contains chairs by Roy McMakin, whose giant furniture she first encountered at the L.A. home of John Baldessari, another artist she collects.

When she moved into her house, Delug worked with the local designer Sarah Walker to create interiors that highlight the art. The sculptor Franz West created her long, slim dining table together with the chairs with woven seats that surround it, while above the bar hangs a video screen playing a cheery animation of city and country scenes by Chiho Aoshima. The integration of art and environment is most evident, though, in the placement of Lawrence Weiner’s text piece Stretched as Tightly as Is Possible: (Satin) & (Petroleum Jelly). When she began remodeling, Delug asked the artist where he would like it situated. His reply: at the bottom of the swimming pool. Without hesitation, she had the pool emptied and the work, unique in the artist’s oeuvre, installed. When Weiner’s retrospective opened at MOCA, Delug hosted the party.