Erivan Haub, the 46-year-old multi-millionaire whose West German supermarket operation last week agreed to buy 42 percent of the U.S. A & P company, is no stranger to American ways.

In the early 1950s, as a young management trainee, he spent a year working in Chicago with the Jewel Tea company and another year in Califorania with a firm called Alpha-Beta. Later, his family bought an estate in Tacoma, Wash., which they still own and use frequently.

Three times, Haub's wife traveled to Tacoma to give birth to the couple's three sons there, all of whom have U.S. citizenship.

"He always had a lot of trust and confidence in the United States," says a press spokesperson for West Germany's Tengelmann group, the company that Haub owns and that now holds a big peice of a very traditional part of America symbolized by the venerable A&P name.

Tengelmann is an umbrella organization that includes a chain of supermarkets under the Tengelmann name, another chain of Kaiser supermarkets, a Kaiser coffee business, a chain of discount stores called "Plus" that also carries mostly food and household items, and a chocolate factory.

Collectively, the firm is the largest grocery chain in West Germany, with a turnover of about five billion marks, or about $2.7 billion, in 1973 and some 2,000 retail outlets here and in Austria.

All of it is family-owned and it has remained that way for 150 years, since the firm was started as a single coffee shop in the Ruhr town of Muehlheim, where the business headquarters remains today.

For a while, an aide says, Haub probably thought of living more or less permanently in the U.S. But in 1969, his uncle. Karl Schmitz-Scholl, died and the role of chief executve of the firm was turned over to Haub.

Tengelmann has 17 vice-presidents, a press spokesperson says, but the firm's management philosophy, its prime source of influence and its only ultimate decision-maker, she says, is Haub, the man who owns it all.

Precisely what influence Haub will have on A&P, or what changes he will suggest or demand, is a matter of much speculation in the industry both here and in the U.S. Company officials say Haub probably has some preliminary ideas but that no decisions will be made or strategy drafted until a team of Tengelmann analysts now in the U.S. return in mid-February.

The Kaiser and Tengelmann markets are generally like American supermarkets, somewhat smaller than the "giant" U.S. markets but wellstocked and attractive to shoppers.

Within industrial circles here, sources note that Tengelmann markets tend to stock perhaps 5,000 different items, as opposed to a few times that number stocked by an eaverage A&P. Thus, they suspect that Haub may seek to narrow A&P's selection, and maybe even close down some of the less profitable stores.

A company official here, however, noted that Haub's technique in handling Tengelmann markets wherever they were not profitable was to transform them into the Plus discount markets.

Though it is widely assumed that the Tengelmann group is reasonably profitable, nobody knows for sure because family-owner businesses here are legally rather private affairs between the owner and the tax authorities.

Haub is the fourth generation within the family to run the operation. Asked about the family activities during the Hitler era, a spokesperson said none of the family s erved in the war and none of the Haub family were Nazi party members.