Radio Planetary Nebulae in the Large Magellanic Cloud
  We present 21 new radio-continuum detections at catalogued planetary nebula
(PN) positions in the Large Magellanic Cloud (LMC) using all presently
available data from the Australia Telescope Online Archive at 3, 6, 13 and 20
cm. Additionally, 11 previously detected LMC radio PNe are re-examined with $ 7
$ detections confirmed and reported here. An additional three PNe from our
previous surveys are also studied. The last of the 11 previous detections is
now classified as a compact \HII\ region which makes for a total sample of 31
radio PNe in the LMC. The radio-surface brightness to diameter ($\Sigma$-D)
relation is parametrised as $\Sigma \propto {D^{ - \beta }}$. With the
available 6~cm $\Sigma$-$D$ data we construct $\Sigma$-$D$ samples from 28 LMC
PNe and 9 Small Magellanic Cloud (SMC) radio detected PNe. The results of our
sampled PNe in the Magellanic Clouds (MCs) are comparable to previous
measurements of the Galactic PNe. We obtain $\beta=2.9\pm0.4$ for the MC PNe
compared to $\beta = 3.1\pm0.4$ for the Galaxy. For a better insight into
sample completeness and evolutionary features we reconstruct the $\Sigma$-$D$
data probability density function (PDF). The PDF analysis implies that PNe are
not likely to follow linear evolutionary paths. To estimate the significance of
sensitivity selection effects we perform a Monte Carlo sensitivity simulation
on the $\Sigma$-$D$ data. The results suggest that selection effects are
significant for values larger than $\beta \sim 2.6$ and that a measured slope
of $\beta=2.9$ should correspond to a sensitivity-free value of $\sim 3.4$.
