The crust of Neutron Stars can be approximated by a highly conducting solid crystal lattice. The evolution of the magnetic field in the crust is mediated through Hall effect, namely the electric current is carried by the free electrons of the lattice and the magnetic field lines are advected by the electron fluid. Here, we present the results of a time-dependent evolution code which shows the effect Hall drift has in the large-scale evolution of the magnetic field. In particular we link analytical predictions with simulation results. We find that there are two basic evolutionary paths, depending on the initial conditions compared to Hall equilibrium. We also show the effect axial symmetry combined with density gradient have on suppressing turbulent cascade.