  The Minkowski content of a compact set is a fine measure of its geometric
scaling. For Lebesgue null sets it measures the decay of the Lebesgue measure
of epsilon neighbourhoods of the set. It is well known that self-similar sets,
satisfying reasonable separation conditions and non-log comensurable
contraction ratios, have a well-defined Minkowski content. When dropping the
contraction conditions, the more general notion of average Minkowsk content
still exists. For random recursive self-similar sets the Minkowski content also
exists almost surely, whereas for random homogeneous self-similar sets it was
recently shown by Z\"ahle that the Minkowski content exists in expectation.
  In this short note we show that the upper Minkowski content, as well as the
upper average Minkowski content of random homogeneous self-similar sets is
infinite, almost surely, answering a conjecture posed by Z\"ahle. Additionally,
we show that in the random homogeneous equicontractive self-similar setting the
lower Minkowski content is zero and the lower average Minkowski content is also
infinite. These results are in stark contrast to the random recursive model or
the mean behaviour of random homogeneous attractors.
