The two main bank players in the U.S. on-line brokerage market posted starkly different results during the third quarter, according to separate studies.

Waterhouse Investor Services, the New York-based broker-dealer unit of Canadian Toronto-Dominion Bank, is making strides in Internet trading, while Fleet Financial Group's Quick & Reilly is losing market share, according to studies from Credit Suisse First Boston and Piper Jaffray.

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