In this paper, we propose country-specific and systemic metrics that can be used to judge whether cross-border banking in a country (or region) takes a desirable form. Applying these metrics to the EU countries, we find that the countries with the largest banking centres, the UK and Germany, are well diversified. By contrast, the New Member States (NMS) are highly dependent on a few West European banks and vulnerable to contagion effects. The Nordic and Baltic regions are closely interwoven with little diversification. At the system level, the EU banking system is weakly diversified, with an overexposure to the United States and an underexposure to Japan and China. This explains why the recent US-originated financial crisis had such a significant impact on European banks.