  Context. We investigate the dynamical evolution of the reconnection process
at an initially linear 3D null point that is stressed by a localised shear
motion across the spine axis. The fan plane is not rotationally symmetric and
this allows for different behaviours depending on the alignment of the fan
plane relative to the imposed driver direction. Aims. The aim is to show how
the current accumulation and the associated reconnection process depends on the
relative orientation between the driver imposed stress across the spine axis of
the null and the main eigenvector direction in the fan plane. Methods. The time
evolution of the 3D null point is investigated solving the 3D non-ideal MHD
equations numerically in a Cartesian box. The magnetic field is frozen to the
boundaries and the boundary velocity is only non-zero where the imposed driving
is for stressing the system is applied. Results. The current accumulation is
found to be along the direction of the fan eigenvector associated with the
smallest eigenvalue until the direction of the driver is almost parallel to
this eigenvector. When the driving velocity is parallel to the weak eigenvector
and has an impulsive temporal profile the null only forms a weak current layer.
However, when the null point is stressed continuously boundary effects
dominates the current accumulation. Conclusions. There is a clear relation
between the orientation of the current concentration and the direction of the
fan eigenvector corresponding to the small eigenvalue. This shows that the
structure of the magnetic field is the most important in determining where
current is going to accumulate when a single 3D null point is perturbed by a
simple shear motion across the spine axis. As the angle between the driving
direction and the strong eigenvector direction increases, the current that
accumulates at the null becomes progressively weaker.
