Geodynamic models of thermo-chemical plumes rising in a mantle wind suggest that we should abandon some paradigms based on the dynamics of purely thermal axisymmetric plumes. The head-tail structure is possible but not unique and the lack of a plume head does not preclude a deep origin. Our results suggest that the surface expression of some thermo-chemical plumes may be a headless, age-progressive volcanic chain. Plume tails are laterally heterogeneous, rather than concentrically zoned, because deep heterogeneities are sheared into distinct and long-lasting filaments that will be successively sampled by different volcanoes, as the oceanic plate moves over the plume tail. Finally, calculated S-wave velocity anomalies are consistent with recent plume tomographic images, showing that compositional heterogeneities in the lowermost mantle favour the coexistence of a great variety of plume shapes and sizes.