A number of recent theoretical studies have explored trading in fragmented markets, e.g. Biais et al. (2000), a phenomenon increasingly witnessed in modern markets. The key assumption generating the results is that there is at least one liquidity demander exploiting access to all markets by optimally splitting orders across markets. This paper seeks to test this assumnption in a natural experiment involving Dutch stocks that are traded both in Amsterdam and New York. The results confirm the presence of rational, order splitting traders. This explains the increased volume and relatively large and persistent price changes for the overlapping period. <BR><BR>