Recent paper by Shin of Princeton, highlighted and linked by Krugman, arguing that the European banking system is acting as a gigantic boom-bust amplifier for the US.
Non-US bank branches that conduct business in dollars act as an element, a very big one, of the shadow banking system.
The paper is detailed. Shin draws this conclusion: "The global flow of funds perspective suggests that the European crisis of 2011 and the associated deleveraging of the European global banks will have far reaching implications not only for the eurozone, but also for credit supply conditions in the United States and capital flows to the emerging economies." Why? In the end the most important thing is that "dollar-denominated assets of banks outside the U.S. are comparable in size to the total assets of the US commercial bank sector."