Intermittent blobs, which propagate across a confining magnetic fields, are universally observed in natural and laboratory plasmas. In fusion plasmas, cross-field transport of particles and energy are associated, at least in part, with the propagation of blobs, which are therefore of great importance for the design of future fusion reactors. In TORPEX, blobs are generated from ideal interchange modes and, driven by B and curvature-induced charge separation, propagate radially outwards. An analytical blob speed-versus–size scaling, including cross-field ion polarization currents, cross-field ion currents due to neutral friction and parallel currents to the sheath, shows quantitative agreement with the experimental data. This suggests that the blob radial velocity is determined by the available current paths (parallel or cross-field currents) to damp charge separation. To confirm this interpretation, we perform direct two dimensional measurements of the field-aligned current associated with blobs, whose ends terminate on a conducting limiter. A dipolar structure of the current density is measured, which originates from ∇B and curvature induced polarization of the blob and is consistent with sheath boundary conditions. The dipole is strongly asymmetric due to the nonlinear dependence of the current density at the sheath edge upon the floating potential. This results in a net current flowing to the limiter. The relevance of the current density asymmetry to filaments observed during edge localized modes is also discussed. For the first time, we directly demonstrate the existence of two regimes, as suggested by the scaling law, in which parallel currents to the sheath do or do not significantly damp charge separation and thus reduce the blob radial speed. Finally, we report on methods to influence and control blob dynamics, such as varying the blob connection length or the use of poloidal arrays of biased electrodes. This work was supported in part by the Swiss National Science Foundation.