This study applies a novel quantile unit root with structural breaks approach to explore whether the international crude oil markets are better characterized as ‘globalized’ or ‘regionalized’. By using the spreads between WTI and Brent crude oil prices as a benchmark, we find that the spreads contain a unit root in the lower quantiles but display mean reversion behaviour in the upper quantiles. However, instead of focusing on some selected (local) quantiles, the quantile Kolmogorov–Smirnov tests over a range of quantiles suggest that the price differentials are universally mean-reverting and, thus, provide strong support to the ‘globalization’ view.