HCA will release as many as 142.6 million shares at a price in the range of $27 to $30 each, according to a filing today. The company aims to sell 87.7 million shares and its owners are offering 36.3 million shares, the filing showed. The underwriters have the option to purchase an additional 18.6 million shares.

The hospital operator, based in Nashville, Tennessee, is trying to go public less than four months after taking on new debt to pay its owners, including KKR & Co., Bain Capital LLC and Bank of America Corp., a $2 billion dividend. Private-equity firms, taking advantage of a rally in leveraged loans and stocks, are stepping up dividend recapitalizations and initial public offerings to return money to investors.

“It’s been a difficult time to bring new companies public,” said Les Funtleyder, an analyst at Miller Tabak & Co. in New York. “This will be a good test of the market to see if it can take an offering this large. If HCA is successful, you’ll probably see a lot more offerings after that.”

HCA had $30.7 billion in revenue in 2010 and net income of $1.57 billion, according to the filing.

HCA first filed for a public offering in May, and refiled in December after selling $1.53 billion of 10.5-year notes to help pay for the dividend. In the May filing, the company said it planned to raise a net $2.5 billion by selling new shares and would use the proceeds to repay debt.

HCA’s owners put up about $5.3 billion to buy the company, according to a regulatory filing, funding the rest with loans from banks, including Charlotte, North, Carolina-based Bank of America; and JPMorgan Chase & Co. and Citigroup Inc., both based in New York. Including the November distribution, the owners paid themselves about $4.3 billion in dividends last year.

HCA operated 164 hospitals and 106 freestanding surgery centers as of Dec. 31, according to a filing.

The underwriters include Bank of America Merrill Lynch, Citigroup and JPMorgan.

The original HCA was founded as Hospital Corp. of America in 1968, when a Nashville physician named Thomas Frist Sr.; his son, Thomas Frist Jr.; and Jack Massey built a hospital and formed one of the first hospital companies in the U.S. Thomas Frist Sr. is also the father of Bill Frist, a physician and a Tennessee Republican who is a former U.S. Senate majority leader.