(FORTUNE Magazine) – AMONG the billionaires, women make up a baker's dozen -- there are four Americans and nine Europeans. These billionairesses are hard to comprehend. Not only are their names unfamiliar for the most part -- not a Du Pont, a Mellon, or even a Rockefeller among them -- but they also take particular pains to preserve their anonymity. Robin Leach, host of TV's Lifestyles of the Rich and Famous, gushes, ''Oh, to know them would be to love them!'' If only anyone could. For example, Barbara Cox Anthony of Atlanta's Cox broadcasting and newspaper dynasty had not spoken with the press for years until she recently told FORTUNE: ''The more anonymous you can be, the better. Why, then you can just do whatever you want.'' Perhaps these women cultivate mystery because no one, including themselves, ! is quite sure how they are supposed to live their lives. Their wealth is so great it's an abstraction, and they are not obliged, as the rest of us are, to earn their keep. Put a billion dollars in a humble NOW account yielding only 5%, and you could skim off $137,000 in interest every glorious day! Many possess more than a mere $1 billion, as the list beginning on page 59 will tell you. Were they men, they would be expected to prove their worth beyond their wealth, perhaps by running the family business. But rich women are rarely bred for that. Nonetheless, a strong work ethic exists in nearly all these heiresses, perhaps because most were fathered by or wedded to the men who built the billions. As daughters or widows, they are intent on proving their own merits, if not in business then in life or in love. Alice Walton, Sam's daughter and his only girl (he also has three sons), insists she doesn't think about her wealth, neatly tied up in about $4 billion of Wal-Mart stock. Her sights are set instead on building her investment bank, Llama Co., named for her favorite animal. A onetime stockbroker with E.F. Hutton, the tall, stylish Walton started her own company (assets: $111 million) three years ago in Fayetteville, Arkansas, to help develop the area's economic base. ''This whole region -- states like Arkansas and Oklahoma -- gets left out by Wall Street and the money center banks,'' she drawls. There's $14 million of Walton's own tucked into Llama Co., relative pennies considering her Wal-Mart wealth but enough to give her a 56% stake in the firm. Underwritten deals through July total $756 million, up from $460 million in the first seven months of 1990. She figures that providing capital for public projects and private factories in the neglected heartland -- for example, helping finance a $200 million recycled linerboard plant in Muskogee, Oklahoma -- is similar to what her father did with his retail stores. ''Wal- Mart grew up by filling a real need,'' she says. ''It gave a broad selection of well-priced merchandise to people in small towns who didn't have access to it.'' Whether you're talking toasters or tax-exempt bonds, says Sam's daughter, ''our philosophies are intertwined.'' EUROPE'S Wal-Mart of mail order, Quelle is a catalogue company based in the Bavarian town of Furth. It sells everything from clothing and china to furniture and electronics at rock-bottom prices. And like the American company, it is associated with a septuagenarian entrepreneur, Grete % Schickedanz. Hired in 1927 at age 15 to work in the company, Grete married the founder, Gustav Schickedanz, 13 years after his wife and son died in an auto accident. A year later, American planes dropped a bomb on Quelle's headquarters, leaving merchandise and customer lists in ashes. When Gustav, a Nazi Party member, was barred from rebuilding his business after the war, Grete took over. Setting up a tiny store, she traveled the country in search of merchandise. Her motto: ''Lost time. Lost money.'' Gustav died in 1977, leaving Quelle in Grete's good hands. A compassionate boss, she has initiated unusual employee benefits, such as low-rent housing for employees and day care for their children. With her 80th birthday approaching October 15, Schickedanz often works an eight-to-six day. East Germans' feverish spending of their new deutsche marks helped push Quelle's sales up 24% last year, to $7 billion. Estee Lauder, the only woman who built her billions from nothing, is another workhorse in creating a business and a fantasy life. Now 83 and elegant always in her Givenchy and Valentino gowns and perfect makeup, she says, ''There wasn't a minute of any day when I didn't look as pretty as I knew how to make myself.'' For decades she promoted a view of herself as born into a wealthy Viennese family who taught her European skin-care techniques. As it turns out, this was just makeup, the dream of a little girl named Josephine Esther Mentzer, born to Jewish immigrant parents in Queens, New York City. Uncle John whipped up face creams over a gas stove, and Esther, a tireless promoter, hounded Saks Fifth Avenue and other top department stores until they bought her product. A born marketer, she invented the gimmick of handing out a free gift with a cosmetics purchase. Says Dominick Dunne, who writes about the upper classes: ''Estee's not just a Le Cirque lady. She made the bucks.'' The right role for a billionairess is not always a corporate one. Though the Cox sisters inherited Cox Broadcasting and the Atlanta Constitution from their father, he believed that women should not be actively involved in business. So, leaving Cox Enterprises to sons and husbands, Anne Cox Chambers found her purpose in politics. ''I was a late bloomer,'' she says. Her friendship and financing helped Jimmy Carter reach the White House, and she was 56 when he made her ambassador to Belgium in 1977. She says, ''I received a check each month from the U.S. government, and I knew that I had earned it.'' ) A frugal streak runs through these females of fortune. The villagers of Tarvanelle, near Queen Beatrix's vacation home in Tuscany, say they have been astounded to see the Dutch monarch, 53, hammering and painting to help restore her modest farmhouse. True, she technically can no longer be considered a billionairess, because this year the government reported that to avoid taxes, she allowed most of her fortune to be tied up in foundations over which she has limited control. Queen Elizabeth II's thrift is legendary. Not only does she have parsimonious lineage, but she is aware that some of her subjects find the monarchy an extravagance. She has a personal fortune of $10.7 billion, which is untaxed, and more than 70% of the public think the 65-year-old Queen should at least pay income tax. As a result she avoids excess. Andrew Morton, who has written several books about the royals, reports that the Queen's Christmas gifts to her family are things like garden gloves, a hot water bottle, sometimes a compass. Elizabeth is not the only royal who realizes that a high-living image is imprudent. Princess Gloria von Thurn und Taxis, the German ''punk princess,'' has been toning it down. No more wild partying, no more midnight rides on her Harley-Davidson in spiked hairdo and Christian LaCroix gowns. At 31, madcap Gloria is matronly in a pageboy hairdo and plain blouses and skirts. The story behind the makeover: Prince Johannes, her husband, died last December at 64. The widow is now the mother of the largest landowner in Europe, Prince Albert, 8, who inherited Johannes's loot. Not only does Gloria feel responsible for putting the mismanaged Thurn und Taxis estate in order for her son, but she is growing up herself as well. ''This change has something to do with age,'' she says. ''If I had continued this extrovert phase at 40, then you could say, 'She is crazy.' '' It's a cliche, of course, but the big burden of billionairedom for these women is finding a man strong enough to love them. The usual questions come up: Does he love me or my money? Can he handle the power that my money gives me? Claus von Amsberg, the former German diplomat who is married to Queen Beatrix, has admitted publicly that he underestimated the challenge of living in her shadow. He suffered from serious depression ten years ago, and a recent relapse has him in The Hague's Bronovo hospital. He makes it home for weekends. Johanna Quandt and her daughter, Susanne, who own 40% of BMW, have fended ; off fortune hunters by building walls around themselves. Susanne, 28, met her husband, Jan Klatten, while working at the automaker under an alias, or so the story in the German press goes, though the family denies it. Yearning to be loved for herself, she revealed her true identity a few months after they met. Johanna, 64, widow of Herbert Quandt, who rescued BMW from near bankruptcy in 1959, has been called ''the nun in the golden convent.'' She avoids parties and is rarely recognized even by locals in her town of Bad Homburg near Frankfurt. But it is possible to luck out in love. Liliane Bettencourt, 68, the only child of Eugene Schueller, the chemist who founded L'Oreal, wed Andre Bettencourt, a promising young politician, in 1950. He rose to become Minister of Posts and Telecommunications and later Minister of Industry. She gained both a good husband and great connections in government circles. When Liliane decided that she was not up to running L'Oreal, Andre recruited his boyhood chum, Francois Dalle, for the job. A brilliant businessman, Dalle has built L'Oreal into the world's largest beauty-products company and made Liliane the richest person in France. THE OTHER French-born billionairess, Chantal Grundig, 42, was a Cinderella. Her prince was German electronics company founder Max Grundig. Hired as a language tutor to Max's second wife, Chantal became Frau Grundig No. 3. The tycoon's death two years ago upset her so greatly that she developed stomach and intestinal disorders, losing 30 pounds. But life goes on. Max's best friend, Dr. Gunther Dietze, treated Chantal with amazing results. The two have become inseparable, and Gunther is said to be divorcing his own wife. Marriage has been good to Heidi Horton as well. She told Bunte, a German weekly magazine, that she was a 26-year-old secretary when she married Helmut Horton, a German department-store tycoon whom she met in a bar. Helmut, 31 years her senior, promptly turned into Henry Higgins, bringing in language tutors, etiquette teachers, and makeup artists to transform Heidi into a lady. Helmut, who never wanted children because he feared they would turn communist, has tried to rein in Heidi from beyond the grave. He died in 1987, and his will stipulates that she may spend only $150 million a year, and she may not give her fortune to three types of men: kidnappers, blackmailers, and future husbands. No matter; the platinum-blond Heidi, 51, is apparently set to wed her beau, Cary, Count Goess of Worthersee, in January. A nobleman with a stylish five-day growth of beard and flair on the dance floor, Cary, 40, is already ensconced in Heidi's Austrian castle. Lucky for him, the deluxe digs house 24 ballrooms. Billions can often breed bad marriages too. Alice Walton and Anne Cox Chambers are both twice-divorced. And then there are the strange affairs of the beautiful Koplowitz sisters. Dark-toned, reserved Esther, 41, and blond, more outgoing Alicia, 39, inherited Construcciones y Contratas, or Conycon, from their father, Ernest. He was a Polish Jew who fled Hitler, arrived penniless in Spain, and founded a construction firm to help rebuild Madrid after the Spanish civil war. THE SISTERS live as if they were the Doublemint twins. In 1969 they married two cousins, both named Alberto. Los Albertos ran Conycon together, building it into one of Spain's largest, most successful companies. Each couple had three children, and the families lived unspectacular lives in identical apartments on the same Madrid block. When tabloids ran photographs of Alicia's Alberto leaving a Vienna hotel with another woman, it was inevitable that Esther's Alberto would be collared too. Last year the synchronous siblings divorced los Albertos, kicked them out of Conycon, and pensioned them off with about $100 million. The women installed themselves as president and vice president of the company; they usually lunch together, and alternate their jobs every 12 months. But are they happy? you ask. Hardly. Alicia, labeled ''SuperBarbie'' by the press and photographed lately with a new man, says: ''It is as if I am in a glass jail. I no longer have any privacy. My life has become a hell . . . That old phrase about 'the poor little rich girl' has a lot of truth.'' Like war, being a billionairess can be hell. But when you ask Anne Cox Chambers whether she ever wanted not to be so rich, she bursts into laughter before giving an honest response. ''No,'' she says emphatically. ''Do any women answer that question any other way?''