The adsorption kinetics of amphiphilic poly(tert-butyl styrene)-block-poly(sodium styrenesulfonate) copolymers have been monitored as a function of a monovalent 1:1 salt (sodium chloride) to hydrophobic octadecylsilane (OTS) surfaces and compared to the adsorption kinetics of poly(sodium styrenesulfonate) homopolymer. The initial adsorption rate of the homopolymer shows a weak power-law dependence on the external salt concentration, phi(s)(1/10), at salt concentrations above 0.01 M, in agreement with diffusion-limited kinetics. Moreover, the adsorbed amount reaches a definitive plateau in less than 24 h at all salt concentrations. The initial adsorption rate of the copolymer, on the other hand, adsorbs 1-2 orders of magnitude more slowly than the homopolymer and does not follow diffusion-limited kinetics, which call be ascribed to the presence of micelles. Micelles adsorb to the surface, but the micelles must overcome a potential energy barrier in order to adsorb. That being said, the copolymer micelles eventually surpass the adsorbed amount of the homopolymer and show no signs of reaching saturation, even after 1 week of adsorption. The copolymer shows two types of adsorption kinetics at long times. If the external salt concentration phi(s) is sufficiently higher than the counterion concentration associated with the adsorbed layer, the copolymers adsorb with phi(s)(2/5){log(t)}(6/5) kinetics. In the other limit, where the internal ion concentration in the brush layer is higher than the external salt concentration, the adsorption kinetics show weak power-law behavior. Simple scaling relationships have been established to understand the qualitative differences between adsorption in the two regimes.