  We present synthetic single-line and continuum linear-polarisation signatures
due to electron scattering in axially-symmetric Type II supernovae (SNe) which
we calculate using a Monte Carlo and a long-characteristic radiative-transfer
code. Aspherical ejecta are produced by prescribing a latitudinal scaling or
stretching of SN ejecta inputs obtained from 1-D non-LTE time-dependent
calculations. We study polarisation signatures as a function of inclination,
shape factor, wavelength, line identity, post-explosion time. At early times,
cancellation and optical-depth effects make the polarisation intrinsically low,
causing complicated sign reversals with inclination or continuum wavelength,
and across line profiles. While the line polarisation is positive (negative)
for an oblate (prolate) morphology at the peak and in the red wing, the
continuum polarisation may be of any sign. These complex polarisation
variations are produced not just by the asymmetric distribution of scatterers
but also of the flux. Our early-time signatures are in contradiction with
predictions for a centrally illuminated aspherical nebula, although this
becomes a better approximation at nebular times. For a fixed asymmetry, our
synthetic continuum polarisation is generally low, may evolve non-monotonically
during the plateau phase, but it systematically rises as the ejecta become
optically thin. Changes in polarization over time do not necessarily imply a
change in the asymmetry of the ejecta. The SN structure (e.g.,
density/ionization) critically influences the level of polarisation.
Importantly, a low polarisation (<0.5%) at early times does not necessarily
imply a low degree of asymmetry as usually assumed. Asphericity influences
line-profile morphology and the luminosity, which may compromise the accuracy
of SN characteristics inferred from these.
