Quick. Name the first five law firms that come to mind.

That’s the question that market research firm Acritas recently asked 1,000 in-house counsel whose companies gross at least $1 billion in revenue. The most common answer: Baker & McKenzie.

Baker & McKenzie’s score in the survey, which ranks firms by four factors—awareness, favorability, multijurisdictional litigation, and multijurisdictional transactional capabilities— was nearly double that of the second-place firm. In 2012 Baker & McKenzie claimed the top spot for the fifth straight year. Freshfields Bruckhaus Deringer was a distant second, followed by Linklaters in third and Clifford Chance in fourth.

A key factor in achieving a high score is a firm’s international presence, says Lisa Hart Shepherd, chief executive officer and founder of Acritas. “Baker has been in South America and Asia and the U.S. for quite a long time, which has built up brand recognition. It’s way ahead of other firms,” says Shepherd. Baker & McKenzie opened its first international office in 1956 in Venezuela, says Eduardo Leite, chairman of the firm’s executive committee, and the firm has been focused on global growth ever since. Baker & McKenzie now has 72 offices in 45 countries.

Some of the fastest-rising firms on Acritas’s 2012 index—number five DLA Piper, which moved up five spots this year, and number nine Norton Rose, which was number 15 in 2011—have either merged or aligned themselves with other international firms over the last two years. DLA merged with its Australian arm, DLA Phillips Fox, in 2011, and the firm formed alliances with firms in Turkey, Brazil, and Kenya in 2010. Norton Rose formed a three-way tie-up with South Africa’s Deneys Reitz and Canadian firm Ogilvy Renault in 2010. “Unless you’re in New York or are a boutique, global wins at the end of the day,” says Peter Martyr, Norton Rose’s chief executive. “That’s the name of the game we’re playing.”

On the flip side, scores for firms that haven’t made international inroads dipped in the last year, mainly because their brand awareness has shrunk as firms with a global presence have secured footholds in growing markets such as Asia and Latin America, says Shepherd. Many of the U.S.–based firms on the list fit this mold; all those that landed in the top 15 saw their scores shrink in 2012.

While U.S. firms’ name recognition might lag behind international firms, the lack of brand recognition apparently hasn’t hurt business. “The philosophy of the New York firms has always been to make money,” says Martyr, and they’ve done so within the confines of the United States. As a result, Martyr says, major U.K. players have been pushed out of the U.S. and into the global market. Baker & McKenzie doesn’t mind the company, says Leite: “We’ll just find the next new jurisdiction and try to be the first one to get there.”