  The open problem of how singular current structures form in line-tied,
three-dimensional magnetic fields is addressed. A Lagrangian magneto-frictional
relaxation method is employed to model the field evolution towards the final
near-singular state. Our starting point is an exact force-free solution of the
governing magnetohydrodynamic (MHD) equations which is sufficiently general to
allow for topological features like magnetic nulls to be inside or outside the
computational domain, depending on a simple set of parameters. Quasi-separatrix
layers (QSLs) are present in these structures and together with the magnetic
nulls, they significantly influence the accumulation of current. It is shown
that perturbations affecting the lateral boundaries of the configuration lead
not only to collapse around the magnetic null, but also to significant QSL
currents. Our results show that once a magnetic null is present, the developing
currents are always attracted to that specific location and show a much
stronger scaling with resolution than the currents which form along the QSL. In
particular, the null point scalings can be consistent with models of "fast"
reconnection. The QSL currents also appear to be unbounded but give rise to
weaker singularities, independent of the perturbation amplitude.
