This theoretical study deals with the Navier-Stokes equations posed in a 3D thin domain with thickness 0 < ε ≪ 1, assuming power law slip boundary conditions, with an anisotropic tensor, on the bottom. This condition, introduced in (Djoko et al. Comput. Math. Appl. 128 (2022) 198–213), represents a generalization of the Navier slip boundary condition. The goal is to study the influence of the power law slip boundary conditions with an anisotropic tensor of order ε^{γ/s} , with γ ∈ R and flow index 1 < s < 2, on the behavior of the fluid with thickness ε by using asymptotic analysis when ε → 0, depending on the values of γ. As a result, we deduce the existence of a critical value of γ given by γs∗ = 3 − 2s and so, three different limit boundary conditions are derived. The critical case γ = γs∗ corresponds to a limit condition of type power law slip. The supercritical case γ > γs∗ corresponds to a limit boundary condition of type perfect slip. The subcritical case γ < γs∗ corresponds to a limit boundary condition of type no-slip.