  Starting from an exact, steady-state, force-free solution of the
magnetohydrodynamic (MHD) equations, we investigate how resistive current
layers are induced by perturbing line-tied three-dimensional magnetic
equilibria. This is achieved by the superposition of a weak perturbation field
in the domain, in contrast to studies where the boundary is driven by slow
motions, like those present in photospheric active regions. Our aim is to
quantify how the current structures are altered by the contribution of so
called quasi-separatrix layers (QSLs) as the null point is shifted outside the
computational domain. Previous studies based on magneto-frictional relaxation
have indicated that, despite the severe field line gradients of the QSL, the
presence of a null is vital in maintaining fast reconnection. Here, we explore
this notion using highly resolved simulations of the full MHD evolution. We
show that for the null-point configuration, the resistive scaling of the peak
current density is close to $J\sim\eta^{-1}$, while the scaling is much weaker,
i.e. $J\sim\eta^{-0.4}$, when only the QSL connectivity gradients provide a
site for the current accumulation.
