When Pablo Picasso died seven years ago, more than 45,000 paintings, sculptures, ceramic objects, sketches and lithographs were found in the three villas he owned on the French Riviera. It was said he would fill up one house, lock the door and buy another. "We'd have to rent the Empire State Building to house all his works," laughs Picasso's son, Claude, 33. No one knows precisely how many exist, but 1,000 of the finest go on exhibit this week (until September 16) at New York's Museum of Modern Art. The show, which includes treasures from private collections and museums in Moscow, Prague, Barcelona, London and Leningrad, is the most comprehensive and important ever mounted of the artist's work.

The plaudits, of course, will go to Pablo, but the event is a triumph, too, for Claude, the shy illegitimate son who has emerged as the overseer of the $260 million Picasso estate. "I'm sort of the goodwill person around town," he shrugs. "I help with information and road maps." He facilitated loans of Picasso masterpieces never before exhibited, photographed works for the MOMA catalogue and came up with replacements when Picasso's widow, Jacqueline, reneged at the last moment on a promise to deliver 17 paintings from her collection. "While the others were happy to lend, Claude gave of himself," says William Rubin, MOMA's director of paintings and sculpture.

For the past six years Claude has presided over negotiations among the five other heirs and their 19 lawyers to put his father's affairs in order. Pablo died at 91 without a will.

While his father was alive, Claude hardly seemed a peacemaker. He and his sister Paloma filed an unsuccessful lawsuit in 1970 to be recognized as Picasso's legal heirs—and reportedly even sought to have their father declared mentally incompetent. Their mother, Françoise Gilot (who is now married to scientist Jonas Salk), had been Picasso's mistress for 11 years before moving out in 1953. "You can't live with a historical monument," she explained. Picasso had told her, "For me there are only two kinds of women—goddesses and doormats." Françoise showed herself to be neither with the publication of her 1964 memoir, Life with Picasso. It so outraged the master that Claude and Paloma, who lived with their mother in Paris and summered with Picasso near Cannes, were barred from his home from that time on. Claude saw his father only a few times more, just before his death.

Shortly before that, French inheritance laws had been changed, permitting Claude and Paloma to be legally recognized as heirs, along with a half sister, Maya, Pablo's daughter by Marie-Thérèse Walter. Picasso's only legitimate child, Paulo, died in 1975, leaving two children, who share in the estate.

Claude's initial scheme was to mass-market bronze editions of his father's metallic sculptures. Later he dropped the idea, sold the Rolls-Royce he had bought as a self-indulgence, and became arbiter and spokesman for the family. "My reaction was not, 'Ah, now I will be rich,' " Claude recalls, "but rather, 'What a responsibility.' " He began to spend long hours in a Paris bank vault, classifying and cataloguing Picasso's works. After each heir had selected a favorite (Claude chose a portrait of himself), the rest were divided by drawing straws. To pay off the inheritance tax, the family donated 3,500 pieces, valued at $63 million, to the French government. That collection will be housed in a special Picasso museum scheduled to open in Paris in late 1981, the 100th anniversary of the artist's birth.

Throughout the complex negotiations, Claude and the others have had to battle Jacqueline Picasso. When the administrator of the estate first arrived at her door in 1973, she declared: "I will not help you. And besides, you are wearing an awful tie."

"I have tried to bring the family together," Claude says. "My father should have done it, and to some extent I have succeeded." Claude's success in sorting out his family's tangled affairs led in 1976 to his election as president of SPADEM, the venerable French society that protects artists' rights. Giacometti, Matisse, Renoir and Pablo himself were former members. Claude is praised by an associate for "the tremendous combination of prestige and insight" he brings to the job. Under his leadership, the membership has doubled. To encourage sympathy for the problems of U.S. artists, Claude has "kicked doors around the Senate. You have laws to protect oil men, so why not artists?" he asks.

Claude might have become one himself—with a camera. At 19, he apprenticed with Richard Avedon for 10 months. Later he experimented with directing, under drama coach Lee Strasberg. "You try all kinds of things when you are young and hopeful," he explains. In 1969 he married an aspiring comedienne, Sarah Lee Schultz, but they were divorced four years later. Last November Claude married an American archeologist, Sydney Russell. They live in a Left Bank apartment with her 10-year-old son, Xavier, and an Abyssinian cat named Mimi.

So far Claude has not hung any of the 240 paintings he inherited from his father. Most will remain in storage, as befits his discreet style of living. He drives a VW Rabbit and a hard bargain. "I'm not going to run around uselessly spending money," Claude says. "It's a matter of choosing your charity. Some people choose themselves. For me, that is not enough."