We investigate the long-run growth of Europe in the world economy. The research covers the first half of the XXI° century. The basic trends that will shape the growth regime in the global economy are the demographic transition and the diffusion of technological progress. We use the framework of INGENUE, an OLG model which divides the world in ten broad regions. Hypotheses are elaborated on the basic trends and discussed in an historical perspective. Structural changes are then introduced into INGENUE to make prospective scenarios. A baseline scenario is built to outline the main macroeconomic features of the broad regions. This scenario being used as a benchmark is deliberately conservative as far as structural and institutional changes are concerned. It depicts Western Europe as an ageing low-growth region, accumulating net foreign assets and enjoying an appreciating real exchange rate. These are the characteristics of a permanent creditor in a world growth regime supported by capital mobility. The frontiers of Europe are investigated in the last part of the paper by means of two alternative scenarios. First it is assumed that EU enlargement accelerates the technological catch-up of Eastern Europe and boosts growth. Second labour mobility is simulated. Because the cost of financing public retirement is higher in Western Europe, a policy of immigration is implemented to eschew the decline of the labour force. Both the beneficial effects on Western Europe and the adverse effects on the regions of emigration are displayed.