The complexation of different single polyelectrolyte (PE) micelles formed by linear diblock copolymers with oppositely charged brushes with varying grafting densities and charge content was studied by means of molecular dynamics simulations using the primitive model. We found that all micelles perform a directed motion along the vertical z axis on the grafted surface where they trapped while on the other axes the motion is restricted in a circle in which the diameter decreases with the increase of the hydrophilic length of the linear diblock copolymer. The motion of micelles is characterized as super diffusion inside brushes with low densities and low charge content. At high grafting densities and charge content the diffusion becomes Fickian or slightly subdiffusive. The number of the absorbed brush chains on the micelle corona increases almost monotonically with the increase of brush grafting density or with the decrease of charge content. The distance from the surface in which the micelle is trapped can be controlled by the charge density along the grafted PE chain. (c) 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 621-631