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The Yellowstone-East Snake River Plain hotspot track has been intensely studied since several decades and is widely considered to result from the interaction of a mantle plume with the North American plate. An integrated conclusive geodynamic interpretation of this extensive data set is however presently still lacking, and our knowledge of the dynamical processes beneath Yellowstone is patchy. It has been argued that the Yellowstone plume has delaminated the lower part of the thick Wyoming cratonic lithosphere. We derive an original dynamic model to quantify delamination processes related to mantle plume-lithosphere interactions. We show that fast (~300 ka) lithospheric delamination is consistent with the observed timing of formation of successive volcanic centres along the Yellowstone hotspot track and requires (i) a tensile stress regime within the whole lithosphere exceeding its failure threshold, (ii) a purely plastic rheology in the lithosphere when stresses reach this yield limit, (iii) a dense lower part of the 200 km thick Wyoming lithosphere and (iv) a decoupling melt horizon inside the median part of the lithosphere.We demonstrate that all these conditions are verified and that ~150 km large and ~100 km thick lithospheric blocks delaminate within 300 ka when the Yellowstone plume ponded below the 200 km thick Wyoming cratonic lithosphere. Furthermore, we take advantage of the available extensive regional geophysical and geological observation data sets to design a numerical 3-D upper-mantle convective model.We propose a map of the ascending convective sheets contouring the Yellowstone plume. The model further evidences the development of a counter-flow within the lower part of the lithosphere centred just above the Yellowstone mantle plume axis. This counter-flow controls the local lithospheric stress field, and as a result the trajectories of feeder dykes linking the partial melting source within the core of the mantle plume with the crust by crosscutting the lithospheric mantle. This counter-flow further explains the 50 km NE shift observed between the mantle plume axis and the present-day Yellowstone Caldera as well as the peculiar shaped crustal magma chambers. [ABSTRACT FROM AUTHOR]