  The nature of the evolution of the magnetic field, and of current sheet
formation, at three-dimensional (3D) magnetic null points is investigated. A
kinematic example is presented which demonstrates that for certain evolutions
of a 3D null (specifically those for which the ratios of the null point
eigenvalues are time-dependent) there is no possible choice of boundary
conditions which renders the evolution of the field at the null ideal.
Resistive MHD simulations are described which demonstrate that such evolutions
are generic. A 3D null is subjected to boundary driving by shearing motions,
and it is shown that a current sheet localised at the null is formed. The
qualitative and quantitative properties of the current sheet are discussed.
Accompanying the sheet development is the growth of a localised parallel
electric field, one of the signatures of magnetic reconnection. Finally, the
relevance of the results to a recent theory of turbulent reconnection is
discussed.
