  We describe a new numerical 3D relativistic hydrodynamical code, the results
of validation tests, and a comparison with earlier, 2D studies. The 3D code has
been used to study the deflection and precession of relativistic flows. We find
that even quite fast jets (gamma~10) can be significantly influenced by
impinging on an oblique density gradient, exhibiting a rotation of the Mach
disk in the jet's head. The flow is bent via a potentially strong, oblique
internal shock that arises due to asymmetric perturbation of the flow by its
cocoon. In extreme cases this cocoon can form a marginally relativistic flow
orthogonal to the jet, leading to large scale dynamics quite unlike that
normally associated with astrophysical jets. Exploration of a gamma=5 flow
subject to a large amplitude precession (semi-angle 11.25dg) shows that it
retains its integrity, with modest reduction in Lorentz factor and momentum
flux, for almost 50 jet-radii, but thereafter, the collimated flow is
disrupted. The flow is approximately ballistic, with velocity vectors not
aligned with the local jet `wall'. We consider simple estimators of the flow
emissivity in each case and conclude that a) while the oblique internal shocks
which mediate a small change in the direction of the deflected flows have
little impact on the global dynamics, significantly enhanced flow emission (by
a factor of 2-3) may be associated with such regions; and b) the convolution of
rest frame emissivity and Doppler boost in the case of the precessed jet
invariably leads to a core-jet-like structure, but that intensity fluctuations
in the jet cannot be uniquely associated with either change in internal
conditions or Doppler boost alone, but in general are a combination of both
factors.
