Two years ago, a Dutch law firm prepared a pitch in Moscow to Russian businesses: Come to the Netherlands and we can help you avoid taxes and keep your assets safe.

"You can rely on our legal system!" the firm, Buren van Velzen Guelen, said in a slide presentation.

Such appeals have worked on a grand scale. Russia's biggest oil, gas, mining, and retail companies—including some run by billionaires close to President Vladimir Putin—have moved tens of billions of corporate assets to the Netherlands and other European countries often used for tax avoidance and capital flight, such as Luxembourg, Cyprus, Switzerland, and Ireland. The firms include OAO Rosneft, OAO Gazprom, OAO Lukoil and Geneva-headquartered Gunvor Group Ltd., which was co-founded by a Putin associate now under U.S. sanctions.