  Aims: We attempt to constrain progenitors of the different types of
supernovae from their spatial distributions relative to star formation regions
in their host galaxies, as traced by H alpha + NII line emission.
  Methods: We analyse 63 supernovae which have occurred within galaxies from
our H alpha survey of the local Universe. Three statistical tests are used,
based on pixel statistics, H alpha radial growth curves, and total galaxy
emission-line fluxes.
  Results: Many more type II supernovae come from regions of low or zero
emission line flux than would be expected if the latter accurately traces
high-mass star formation. We interpret this excess as a 40% `Runaway' fraction
in the progenitor stars. Supernovae of types Ib and Ic do appear to trace star
formation activity, with a much higher fraction coming from the centres of
bright star formation regions than is the case for the type II supernovae. Type
Ia supernovae overall show a weak correlation with locations of current star
formation, but there is evidence that a significant minority, up to about 40%,
may be linked to the young stellar population. The radial distribution of all
core-collapse supernovae (types Ib, Ic and II) closely follows that of the line
emission and hence star formation in the their host galaxies, apart from a
central deficiency which is less marked for supernovae of types Ib and Ic than
for those of type II. Core-collapse supernova rates overall are consistent with
being proportional to galaxy total luminosities and star formation rates;
however, within this total the type Ib and Ic supernovae show a moderate bias
towards more luminous host galaxies, and type II supernovae a slight bias
towards lower-luminosity hosts.
