  Let $U\not\equiv \pm\infty$ be a $\delta$-subharmonic function on a closed
disc of radius $R$ centered at zero. In the previous two parts of our paper, we
obtained general and explicit estimates of the integral of the positive part of
the radial maximum growth characteristic ${\mathsf M}_U(t):=
\sup\bigl\{U(z)\bigm| |z|=r\bigr\}$ over the increasing integration function
$m$ on the segment $[0, r]\subset [0,R)$ through the difference characteristic
of Nevanlinna and the quantities associated with the integration function $m$.
The third part of our paper contains estimates of these quantities in terms of
the Hausdorff $h$-measure and $h$-content of compact subset $S\subset [0, r]$
such that the integration function $m$ is constant on each open component of
the connectivity of the complement $[0, r]\setminus S$. The case of the
d-dimensional Hausdorff measure is highlighted separately.
