The recent evolution of continental runoff is still an open question. A related and controversial question is the attribution of this change and its consequences on our predictions of the behavior of future runoff. Here, the Land Surface Model Organizing Carbon and Hydrology in Dynamic Ecosystems is used to perform a set of transient simulations of the runoff from 1900 to 2100. We first show that the model's simulated runoff increases for the 20th century from a global point of view as well as its geographical pattern changes are close to the observations made in this paper. Moreover this trend is simulated to increase further during the 21st century under the SRES A2 scenario. We have designed a set of simulations to test the impact on global runoff evolution of three factors: climate, stomatal conductance, and vegetation growth, all sensitive to CO2 increase. A complete factor-separation analysis of the influence of these three factors and of their interactions shows that climate change largely drives the 20th and 21st century runoff increase. The other two factors (stomatal conductance and vegetation growth) play a minor role in the 20th century runoff trend but we show that these contributions increase for the 21st century simulations. Although the interactions between the factors also plays a negligible role in the 20th century global runoff increase, our results show that they become significant during the 21st century, usually reducing the direct effect of each factor. However, our study does not reveal any important negative feedback to counteract the effect of climate warming on the hydrological cycle.