  Context: The majority of studies on stressed 3D magnetic null points consider
magnetic reconnection driven by an external perturbation, but the formation of
a genuine current sheet equilibrium remains poorly understood. This problem has
been considered more extensively in two-dimensions, but lacks a generalization
into 3D fields.
  Aims: 3D magnetic nulls are more complex than 2D nulls and the field can take
a greater range of magnetic geometries local to the null. Here, we focus on one
type and consider the dynamical non-resistive relaxation of 3D spiral nulls
with initial spine-aligned current. We aim to provide a valid
magnetohydrostatic equilibrium, and describe the electric current accumulations
in various cases, involving a finite plasma pressure.
  Methods: A full MHD code is used, with the resistivity set to zero so that
reconnection is not allowed, to run a series of experiments in which a
perturbed spiral 3D null point is allowed to relax towards an equilibrium, via
real, viscous damping forces. Changes to the initial plasma pressure and other
magnetic parameters are investigated systematically.
  Results: For the axi-symmetric case, the evolution of the field and the
plasma is such that it concentrates the current density in two cone-shaped
regions along the spine, thus concentrating the twist of the magnetic field
around the spine, leaving a radial configuration in the fan plane. The plasma
pressure redistributes in order to maintain the current density accumulations.
However, it is found that changes in the initial plasma pressure do not modify
the final state significantly. In the cases where the initial magnetic field is
not axi-symmetric, a infinite-time singularity of current perpendicular to the
fan is found at the location of the null.
