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The nature of the evolution of the magnetic field, and of current sheetformation, at three-dimensional (3D) magnetic null points is investigated. Akinematic example is presented which demonstrates that for certain evolutionsof a 3D null (specifically those for which the ratios of the null pointeigenvalues are time-dependent) there is no possible choice of boundaryconditions which renders the evolution of the field at the null ideal.Resistive MHD simulations are described which demonstrate that such evolutionsare 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. Thequalitative and quantitative properties of the current sheet are discussed.Accompanying the sheet development is the growth of a localised parallelelectric field, one of the signatures of magnetic reconnection. Finally, therelevance of the results to a recent theory of turbulent reconnection isdiscussed.

Current sheet formation and nonideal behavior at three-dimensional magnetic null points