The London stock index was up slightly while Frankfurt, London and Shanghai were little changed and Tokyo retreated. Wall Street futures were stable ahead of the open.
The House vote sends Trump's case to the Senate for trial. Republicans who control the Senate say they plan to acquit him.
The outcome will be “greater polarization, and a rapid Senate dismissal of the charges made in the House, and then even greater polarization,” Rabobank said in a report.
In Europe, London's FTSE 100 was up less than 0.1% at 7,541 and Frankfurt's DAX was down 0.6% at 13,148. France's CAC 40 shed 0.2% to 5,946.
On Wall Street, futures for the benchmark Standard & Poor's 500 index and the Dow Jones Industrial Average were flat.
The S&P closed up Wednesday less than 0.1% while the Dow dropped 0.1%. The Nasdaq composite rose 0.1% to a record.
In Asia, the Shanghai Composite Index closed at 3,017.07 and Tokyo's Nikkei 225 lost 0.3% to 23,864.85. Hong Kong's Hang Seng sank 0.3% to 27,800.49.
Seoul's Kospi was off 2 points at 2,195.56 and Sydney's S&P-ASX 200 lost 0.3% to 6,833.10.
The Bank of Japan left its short-term policy rate unchanged at -0.1% and its target for 10-year government bond yields at 0%. The Bank of England also left its key rate unchanged, at 0.75%, as it monitors the impact of Brexit on the economy.
ENERGY: Benchmark U.S. crude lost 3 cents to $60.90 per barrel in electronic trading on the New York Mercantile Exchange. The contract declined 2 cents on Wednesday to close at $60.85. Brent crude, used to price international oils, shed 7 cents to $66.10 per barrel in London. It added 7 cents the previous session to $66.17.
CURRENCY: The dollar edged down to 109.50 from 109.56 yen the previous day. The euro was steady at $1.1114.