THE warm Mediterranean night air embraces the dozen or so fans surrounding the tall man outside Rome's Sports Palace."You were great tonight," shouts a woman, as Rick Mahorn signs autographs. The Connecticut native, who plays center for Messaggero Roma, is one of 59 Americans playing with Italy's 32 top-ranked basketball teams. On this fall evening, he helped Messaggero to a 98-86 win over Ranger Varese. Perhaps 100 Ranger Varese fans (Varese is 430 miles north of Rome) sat together in the attractive arena designed by Pier Luigi Nervi for the 1960 Olympic Games. Although they clapped, sang, shouted, and chanted encouragement, the gap in the score opened soon after play began and never closed. About 2,000 Roman fans - clad in a rainbow of pastel-colored polo shirts - watched in relative silence, erupting in cheers and applause only after their players scored. "Basket," as the sport is known here, draws 2.5 million Italian spectators each year, making it Italy's second sport after the phenomenally popular soccer. Basket began to take off about five or six years ago, when Italian and foreign industrialists realized they could garner television, radio, and newspaper publicity by sponsoring teams, says a spokesman for the Italian Basketball Federation. From the corporate point of view the teams are not so much profit-making ventures as a goodwill investment. The result is that leading teams such as Messaggero (owned by the Rome-based newspaper of that name) and Benetton (owned by the clothing manufacturer) spend millions of dollars annually to pay their players and promote their games. "The pay's great," Mr. Mahorn affirms. In fact, the salaries are so large - often two or three times what players a little past their prime had been receiving from the National Basketball Association (NBA) in the United States - that Gianni De Michelis, the president of the country's basketball league (and also the nation's foreign minister), has called for salary caps, in line with the NBA practice of limiting a team's annual payroll to $12.5 million. The smaller teams that can't afford to pay huge salaries support Mr. De Michelis, but the vice president of the league and the larger teams oppose salary caps. Generous paychecks are needed, they say, to attract big-name players. And, they point out, nobody talks about limiting the remumeration of soccer players. "It's necessary to pay the great American players extremely well, especially the centers," Petar Skansi, Benetton's coach, said recently. "And even then they often won't come to Italy, because they live in the legend of the NBA. They prefer to stay with their league, even if it means taking less money." While the Italian league and others benefit from having American players with NBA experience, it's a two-way street: More and more overseas players play in the United States. Among the more prominent of the NBA's foreign-born talents are Nigeria's Akeem Olajuwon (Houston), Yugoslavia's Vldade Divac (Los Angeles Lakers), and the Soviet Union's Sarunas Marciulionis (Golden State), who is joined this year by Alexander Volkov (USSR) of Atlanta. Stojan Vrankovic (Boston) and Drazen Petrovic (New Jersey) join Divac in representing Yugoslavia. Others, like Indiana's Detlef Schrempf (Germany) and Philadelphia's Manute Bol (Sudan), also played US college ball. Italy first allowed foreign players onto its basketball teams in 1965, with a limit of one to a team. In 1976, the ceiling was raised to two foreign players a team. Often they come to Italy from the NBA. Many have several years experience as NBA players: Darryl Dawkins and Bob McAdoo (14 years each), Reggie Theus (13 years), and Mahorn (11 years), for example. But playing here is not easy at first, says Eddie Lee Wilkins, center for Ranger Varese and another former NBA player. "It's an adjustment" to leave the NBA to play for an Italian team and to live in a country with a different culture and language, he says. Mahorn cites another adjustment: Italy's season is less hectic. During the US season, NBA teams may play 100 games. In Italy, he says, they will play about two a week this season (which stretches from Sept. 22 to May 12). "It's not as hard on the body," Mahorn says. US players here find the quality of their teammates is high. When it comes to international basketball, Italians are considered by some to be right behind the Americans. And they learn moves from the NBA all the time, says Mario Arceri, vice president of the Association of Italian Basketball Journalists. "There are very good guys on our team," agrees Mr. Wilkins.