Strengthening economic, social and territorial cohesion is a central objective of the European Union. However, disparities among European regions are considerable, and there are doubts if they are likely to reduce. In recent years there has been an increasing literature examining the effectiveness of the European Union's funds for promoting growth and reducing asymmetries between Members. In this article we contribute to the literature by examining under which conditions European Union financial aid may be affecting regional growth. Doing so, we explore the interactions between transfers and income and other regional characteristics, such as human capital or innovation. The study is applied to a panel of 137 European regions, covering the period 1995-2009. The conclusions suggest a positive and significant marginal impact of Funds only in regions with low levels of human capital and innovation.