NEW YORK, March 15 (Reuters) - Shares of BofI Holding, Inc. (NASDAQ:BOFI) finished their market debut flat on Tuesday after the Internet bank used an auction to price its initial public offering.

Shares of (NASDAQ:BOFI), the parent company of Bank of Internet USA, opened at $11.65 but finished the session at $11.50, even with their IPO price of $11.50.

The company had filed for an offering of 2.25 million shares in the estimated range of $9 to $13 per share. The IPO ended up pricing 3.052 million shares -- raising a more-than-expected $35.1 million.

In traditional IPOs, investment banks use their own discretion to price the deal after gauging investor demand, typically leaving room for shares to rise in their first day of trading.

But BofI used an auction run by W.R. Hambrecht + Co. to sell its shares to the public.

In auctions, potential buyers submit bids for the number of shares they wish to buy and at what price. The IPO is then set at the "clearing price," or the highest price that sells all of the shares being offered, minimizing the first-day "pop" seen in traditional IPOs.

Google Inc. (GOOG.O: Quote, Profile, Research) used a version of an auction to sell its shares to the public last year, and mutual fund and stock research firm Morningstar Inc. has said it will use an auction format for its proposed IPO.