This paper studies convergence in per-capita GDP across European regions over the period 1980--1996. We use median unbiased estimators of the rate of convergence to the steady-state growth path, while allowing for unrestricted patterns of heterogeneity and spatial correlation across regions. By permitting the model parameters to be completely different across regions, not only we avoid imposing strong a priori assumptions but we are also able to analyze the spatial patterns in the estimated coefficients. Our results differ from those found using conventional estimators. The main differences are: i) the mean rate of convergence is much lower; ii) for most regions this rate is zero; iii) the number of regions for which we reject equality in trend growth rates is substantially lower. We also find significant evidence of correlation of growth rates across neighbor regions and across regions belonging to the same country.