The pools control about 512 million shares per day in trades, or about 10 percent of all equity shares traded in the United States, according to data compiled by the Tabb Group.

Nearly every major Wall Street institution seems to have a system in place, from Goldman Sachs' Sigma X and Merrill Lynch's Block Alert to the consortium-owned BIDS network, whose principals include Bank of America, Bear Stearns, and Deutsche Bank.

Each system has its own character, with some allowing negotiated prices and others setting prices based on the quotes in the public markets. Some systems only allow large orders, while others will mix small orders in the trades. A few—worried about manipulation—won't let hedge funds in the door. But others welcome them because they bring liquidity.

Hedge funds were early adopters of the computer algorithms used to find and exploit price discrepancies in dark pools. These algorithms are now so important to the business that Citigroup recently developed a new one, called I.S. Shadow, just to assuage the concerns of two funds that weren't able to complete enough of the profitable trades they had found.

Backers of the pools are attracted to the game because it is lucrative. By satisfying orders internally, they not only avoid stock exchange trading fees but also get paid to make the trades.

Liquidnet, for instance, reported an average daily volume of nearly 57 million shares in the U.S. during the first quarter of 2007, a 28 percent increase from the same quarter in 2006. This seven-year-old company has become the ninth-largest broker on the New York Stock Exchange and is estimated to be worth more than $2 billion.

The Tabb Group predicts that these internal crossing networks and internal markets will continue to eat into the market share of the public exchanges, trading nearly 1.5 billion shares per day by 2010, an annual growth rate of more than 40 percent. That would equal about 15 percent of all equity shares traded in the United States.

By comparison, the N.Y.S.E.'s market share is expected to fall to 32 percent in 2010, from about 40 percent this year, while the Nasdaq is expected to lose just over six percentage points of its current market share over that period, falling to 34 percent.

Public exchanges have been fighting back with plans for their own anonymous-trading systems.

At the same time, Catherine Kinney, the N.Y.S.E.'s president, has attempted to rally opposition to dark pools. She has argued in conferences that private exchanges are already hurting investors by reducing the information that public markets use to set stock prices.