  This paper considers the current distributions that derive from finite
amplitude perturbations of line-tied magnetic fields comprising hyperbolic
field structures. The initial equilibrium on which we principally focus is a
planar magnetic X-point threaded by a uniform axial field. This field is
line-tied on all surfaces but subject to three-dimensional (3D) disturbances
that alter the initial topology. Results of ideal relaxation simulations are
presented which illustrate how intense current structures form that can be
related, through the influence of line-tying, to the quasi-separatrix layers
(QSLs) of the initial configuration. It is demonstrated that the location
within the QSL that attracts the current, and its scaling properties, are
strongly dependent on the relative dimensions of the QSL with respect to the
line-tied boundaries. These results are contrasted with the behavior of a
line-tied 3D field containing an isolated null point. In this case, it is found
that the dominant current always forms at the null, but that the collapse is
inhibited when the null is closer to a line-tied boundary.
