Economic projections for the world economy, particularly in relation to the construction of Computable General Equilibrium (CGE) baselines, are generally rather conservative and take scant account of the wide range of possible evolutions authorized by the underlying economic mechanisms considered. Against this background, we adopt an open mind to the projection of world trade trajectories. Taking a 2035 horizon, we examine how world trade patterns will be shaped by the changing comparative advantages, demand, and capabilities of different regions. We combine a convergence model fitting three production factors (capital, labor and energy) and two factor-specific productivities, alongside a dynamic CGE model of the world economy calibrated to reproduce observed elasticity of trade to income. Each scenario involves three steps. First, we project growth at country level based on factor accumulation, educational attainment and efficiency gains, and discuss uncertainties related to our main drivers. Second, we impose this framework (demographics, gross domestic product, saving rates, factors and current account trajectories) on the CGE baseline. Third, we implement trade policy scenarios (tariffs as well as non-tariff measures in goods and services), in order to get factor allocation across sectors from the model as well as demand and trade patterns. We show that the impact of changing baselines is greater than the impact of a policy shock on the order of magnitude of changes in world trade patterns, which points to the need for care when designing CGE baselines.