The charge distribution in a relativistic double layer is such that the "surface" charge density at the anode appears independent of the thickness of the double layer; in this respect, the double layer is similar to the charge distribution in a capacitor.
The charge distribution in a relativistic double layer is such that the charge density is located in two very thin layers, and inside the double layer the density is constant at and very low compared to the rest of the plasma. In this respect, the double layer is similar to the charge distribution in a capacitor.