  Context: MHD waves and magnetic null points are both prevalent in many
astrophysical plasmas, including the solar atmosphere. Interaction between
waves and null points has been implicated as a possible mechanism for localised
heating events. Aims: Here we investigate the transient behaviour of the Alfven
wave about fully 3D proper and improper 3D magnetic null points. Previously,
the behaviour of fast magnetoacoustic waves at null points in 3D, cold MHD was
considered by Thurgood & McLaughlin (Astronomy & Astrophysics, 2012, 545, A9).
Methods: We introduce an Alfven wave into the vicinity of both proper and
improper null points by numerically solving the ideal, $\beta=0$ MHD equations
using the LARE3D code. A magnetic fieldline and flux-based coordinate system
permits the isolation of resulting wave-modes and the analysis of their
interaction. Results: We find that the Alfven wave propagates throughout the
region and accumulates near the fan-plane, causing current build up. For
different values of null point eccentricity, the qualitative behaviour changes
only by the imposition of anisotropic pulse dilation, due to the differing
rates at which fieldlines diverge from the spine. For all eccentricities, we
find that the fast and Alfven waves are linearly decoupled. During the driving
phase, an independently propagating fast wave is nonlinearly generated due to
the ponderomotive force. Subsequently, no further excitation of fast waves
occurs. Conclusions: We find that the key aspects of the theory of Alfv\'en
waves about 2D null points extends intuitively to the fully 3D case; i.e. the
wave propagates along fieldlines and thus accumulates at predictable parts of
the topology. We also highlight that unlike in the 2D case, in 3D Alfven-wave
pulses are always toroidal and thus any aspects of 2D Alfven-wave-null models
that are pulse-geometry specific must be reconsidered in 3D.
