THE BARON Hans Heinrich Thyssen-Bornemisza de Kaszon is a collectors' collector.

He owns what is considered to be the world's finest collection of old masters still in private hands, and he came to Washington last week to watch a fraction of his fabled holdings become a major enhibition: "Old Master Paintings from the Collectin of Baron Thyssen-Bornemisza," which goes on view at the National Gallery today.

The Baron inherited his title through his mother, a Hungarian baroness who married the German iron and steel heir, Heinrich Thyssen, early in the century. His father became a baron one year later, fled Bela Kuhn to Holland and then settled into Villa Favorita in Lugano, Switzerland, where he founded the collection in the late '20s and '30s.

"But the title means nothing to me," says Thyssen, 58, passing his hand over the long, thinning brown hair slicked straight back in the old European fashion.

"If you have a kingdom, then you have responsibilities, but I am nothing now. I am not a baron because Hungary is a communist country. And as a Swiss citizen, I am nothing because the Swiss have no titles. People call me 'Baron' because it's more chic -- or 'the Baron' when they don't know my name."

"My wife, however, does not agree with my theory that I have no title," he says with an indulgent smile. Denise, his reed thin, much younger fourth wife of a dozen years, calls him "Heine."

"I have an old friend," Thyssen said, "who always introduces me by saying 'this is Heine Thyssen, the iron and steel baron. His mother irons and his father steals.'"

Thyssen also collects houses. In addition to the Villa Favorita, where his collection of 500 old masters is kept, there are the chalet in St. Mortiz, the beach houses in Sardinia, Jamaica and Spain, and the 12-seater Mystere jet with gold faucets that shuttles him back and forth. And of course there is his main residence -- a country house outside Oxford called Daylesford.

But for all his real estate, Thyssen spends much of his time in hotels -- not surprising, in view of his demanding business and collecting schedules. In September, he was at Claridge's, London, because of redecoration at Daylesford, and because he was leaving for Australia the next morning to attend the opening of a touring exhibition of 106 paintings from his collection of modern Americans and Europeans. He was gloating over a new acquistion: a Daumier he'd wanted for a long time. "I was underbidder for that painting four years ago. Today I got it for less than I offered then." t

Thyssen claims he divides his time in thirds: business interests, collection and the family. A few years ago he added an American industrial conglomerate, Indian Head, to his European holdings in banking, shipping, shipbuilding and gas distribution. Indian Head is said to be worth close to $500 million, and represents, according to the Baron, one half of his total business interests. He also says that he hold only $500 worth of stock in Thyssen Steel, the giant combine that made his grandfather the Andrew Carnegie of Europe.

And is he in oil? "Only in oils," he said, obviously delighted with his joke.

"I'd love to stop collecting -- it costs so much money," he complained. "But it's slowing down. It's difficult to find good pictures, and all the dealers try to take advantage and get the highest price possible. I argue on occasion." He buys roughly 20 paintings a year -- old masters and moderns -- and said he feels that "20 is enough." There is no Hirshhornian passion here.

It is the vast range of Thyssen's collecting that distinguishes him from others, most of whom concentrate on the old or the new, the Europeans or the Americans, on paintings or decorative arts. He buys them all. What he'd like is a Leonardo da Vinci, "but I won't get it because there are none. I tried for 15 years to get the Prince of Liechtenstein's Leonardo, and he promised he wouldn't sell it to the National Gallery. But he did, for more than $5 million." The Baron said he would not have paid that price.

Thyssen has advice for would-be collectors: "Buy what you like and don't be afraid to make mistakes." Has he made mistakes? He slapped his knee and laughed, thinking that the subject was his former wives. "If you mean in art, I bought an Otto Muller that was a fake, and of course some things have turned out to be 'school of.' And I don't know all my mistakes yet.

But you must be clever -- you can get good and bad advice. The story of the Kingston Tureens was typical," he said, alluding to his sensational joint purchase, with the Cleveland Museum, of the most famous, most expensive ($1.5 million) silver tureens ever sold at auction. They were made by the 18th-century French silversmith, Meisonnier.

"I was interested in those tureens, and Sherman Lee, director in Cleveland, phoned me in Sao Paulo to ask if I wanted to buy them jointly. We agreed, but all of a sudden there were big articles everywhere saying they were fakes. I was even told that the Louvre had sent three experts who unanimously agreed they were fakes. A half hour before the auction, I asked Lee, 'Shall we still do it?' We did, and guess who the underbidder was? The Louvre."

It turns out you can't always rely on the Baron's reportage either. Christie's Geneva silver expert Richard Stern says "absolutely, the Louvre was not the underbidder for the Kingston Tureens. It was a private Swiss collector."

In art collecting, "you can get swindled, and you can't rely on anybody," said Thyssen, who now makes all of his own decisions about what to buy.

Thyssen decided to bring 57 of his old masters here for two years and nine museums because "I thought I should say 'yes' to America once in my life. There have been requests for many years, but for a long time I had the case pending against the government, and I thought I shouldn't do it then."

Thyssen is obviously still bitter about "Bank for Handel on Scheepvaart v. Robert Kennedy, Attorney General," which was pending in the D.C. Court of Appeals from 1949 until 1961, when the court decided against the Baron. "They called me an enemy of America because I was Hungarian," he said, his cheeks reddening.

The Justice Department tells a different story. During World War II, the American-based bank was confiscated by the government under the Trading With the Enemies Act. Thyssen's father was branded an enemy because the court found that -- although he was a neutral living in Switzerland -- he was proven to have had major interests in a variety of German industrial concerns, including Thyssen Steel, Flensburger Shipyard and Bremer Vulkan Schiffbau-und Maschinenfabrik, which built 74 submarines for the German Navy during World War II. Thyssen still owns the latter.

"Because his father was ultimately the owner, his principal asset in the U.S., the bank, was confiscated," said a Justice Department official. The present Baron (by then his father's heir) brought suit after the war to regain the property, valued at $5 million. He lost.

Some say Thyssen is parsimonious and philanthropy is clearly not his major concern. "We did a lot for Hungarian refugees after the 1956 revolution, and established a home for students in Innsbruck," said the Baron. "We also published a Bible for the refugees in Hungarian."

"I am a Catholic" he explained, "but of course I'm divorced so I was excommunicated." He simply shrugged, this hotel-bound, non-baron, non-Catholic, non-resident of Lugano.

And what will he do with all his modern paintings, which number more than 500? "Many museums have asked to borrow them, including American museums," he said, adding emphatically, "I am not building a wing at Villa Favorita. They're building a museum of modern art in Lagano and some of the paintings will go there." Thyssen and the southernmost, Italian-speaking canton of Switzerland, the Ticino, have been at gentlemanly odds for some time, and bargaining chips are exchanged grudgingly.

A few years back, when the canton imposed a transaction tax Thyssen and others considered confiscatory, he simply moved his official headquarters to Monte Carlo, where he pays no taxes. "We can't lose a Baron Thyssen every day," confided one Ticinese official.

The law has since been repealed, but Thyssen has now established his residence in England, where he is taxed only on income. He has no income in England.

Lagano's profound interest in the baron was clear in the large delegation from that city which came to Washington for the opening, including the mayor and his wife and two high officials of the Ticinese government. But the baron also had an interest in them: He picked up their expenses. "They like to make some propaganda for the Ticino, so they come," he said, dismissing his largesse with a wave of his hand.