For three years, Hong Kong led the world in initial public offerings and international law firms piled in to get a piece of the action. But the market started slowing down late last year, and things haven’t picked up. So far in 2012, the formerly No. 1 Hong Kong Stock Exchange ranks only ninth in the world in terms of funds raised in IPOs, according to statistics from Dealogic.

But meanwhile, another Asian city has come from far behind to become the region’s IPO champ. Kuala Lumpur’s Bursa Malaysia, 15th in the world last year, so far ranks third this year, behind only the two major U.S. exchanges, the New York Stock Exchange and Nasdaq. The $3.3 billion listing in June of Malaysian palm oil company Felda Global Ventures Holdings Bhd. was 2012′s second-largest after Facebook Inc. Last month Kuala Lumpur also saw the $2 billion IPO of hospital chain IHH Healthcare Bhd. A $1 billion debut for port operator Westports Malaysia is expected later in the year.

So is Kuala Lumpur the next big thing?

“It really is the only game in town now, so it’s getting a lot of attention,” says Matthew Bersani, the Asia managing partner for Shearman & Sterling. But it’s also all relative: “The rest of the [capital markets] world is dead, so by comparison it looks great.”

Indeed, Malaysia’s $5.8 billion in IPOs so far this year isn’t so impressive compared to the $31.4 billion Hong Kong IPOs raised last year. If year-to-date figures for the Shenzhen Stock Exchange’s main board and its Chinext growth-stock market are combined, they total almost $9 billion, which looks certain to end up considerably down from last year’s $26 billion.

Bersani notes that Felda is state-owned and IHH is majority-owned by Malaysian sovereign wealth fund Khazanah Nasional Bhd., a fact that may have boosted investor confidence. State funds have invested heavily in the country’s stock market, which the government is pushing to deepen, but Bersani thinks it is unlikely to be a long-term phenomenon.

“Malaysia has had a good year given its state-mandated deals, but those don’t go on forever,” says Bersani.

Chei Liang Sin, a Singapore partner at Latham & Watkins, says the fact that offerings are being led by state-owned enterprises means that the market is still developing; a more mature market would see more private listings.

“Whether or not it can compete with markets like Hong Kong, or even Singapore, over a longer period of time is yet to be seen,” she says.

Moreover, investors don’t look at all SOEs the same way.

“The possible demand for Malaysian IPOs is still a lot less compared to Chinese SOEs of Hong Kong IPOs,” says Sin. “It’s just not a comparable scenario.”

Cleary Gottlieb Steen & Hamilton counsel Robert Williams agrees that comparisons with Hong Kong are a stretch but says there are still worthwhile opportunities for international firms in Malaysian capital markets. Williams was part of a team from Cleary that advised Felda on its IPO. He is confident the pipeline of Malaysian IPOs will continue to be a bright spot this year for the firm, which has an informal Malaysia practice led by Hong Kong partner Sung Kang.

Other major international firms targeting Malaysia work include Magic Circle firms Clifford Chance and Linklaters. Baker & McKenzie has a Malaysian affiliate firm, Wong & Partners, and leading Singapore firm Allen & Gledhill has an alliance with Kuala Lumpur’s Rahmat Lim & Partners.

Among other deals in the works, television operator Astro All Asia Networks Plc. and power company Malakoff Corp. Bhd. are both planning to list in the next year or so. Malakoff recently lined up banks for its $1 billion offering, while Astro All Asia Networks, partly owned by Khazanah Nasional, is seeking regulatory approvals for a $1.5 billion issue.

According to Williams, Cleary is also advising some other blue-chip Malaysian companies on possible IPOs. “These are companies that have listed before and then delisted, and are now looking to relist again,” he says. “And many of them are big household names.”

Those excited about a Malaysia practice may soon have a tough choice to make. Foreign firms are currently barred from having offices in the country. But though the regulatory framework is not yet in place, the country’s Legal Professions Act was amended in April to eventually allow foreign law firms to set up offices and practice in Malaysia via partnerships with a local firm or by obtaining a qualified foreign law firm license.

With many firms already in nearby Singapore, a Kuala Lumpur office could be hard to justify. Bersani says he doesn’t think the recent IPO activity yet warrants a shift in resources.

Williams also doesn’t see the status quo changing at Cleary, which has no Singapore office and covers Southeast Asia out of Hong Kong. “I know we are a little unusual doing Malaysia work out of Hong Kong,” he says, “but we are used to the traveling, so I think it’s going to stay that way for now.”