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  1. Abstract We present high-resolution 2D and 3D simulations of magnetized decaying turbulence in relativistic, resistive magnetohydrodynamics. The simulations show dynamic formation of large-scale intermittent long-lived current sheets being disrupted into plasmoid chains by the tearing instability. These current sheets are locations of enhanced magnetic-field dissipation and heating of the plasma. We find magnetic energy spectra ∝ k −3/2 , together with strongly pronounced dynamic alignment of Elsässer fields and of velocity and magnetic fields, for strong guide-field turbulence, whereas we retrieve spectra ∝ k −5/3 for the case of a weak guide-field.