Interesting heretical findings on order flow implications in a new paper:
We study the rivalry between Euronext and the London Stock Exchange (LSE) in the Dutch stock market to test hypotheses about the effect of market fragmentation. As predicted by our theory, the consolidated limit order book is deeper after entry of the LSE. Moreover, cross-sectionally, we find that a higher trade-through rate in the entrant market coincides with less liquidity supply in this market. These findings imply that (i) fragmentation of order flow can enhance liquidity supply and (ii) protecting limit orders against trade-throughs is important.