  Let $U\not\equiv \pm\infty$ be the difference of subharmonic functions, i.e.,
a $\delta$-subharmonic function, on a closed disc of radius $R$ centered at
zero. In the preceding first part of our paper, we obtained general estimates
for 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 $[0, r]$ via the Nevanlinna
difference characteristic and the modulus of continuity of the function $m$.
The second part of the work gives an explicit view for such estimates, provided
that the modulus of continuity of the function $m$ does not exceed some
differentiable function $h$ on the open interval $(0,r)$ with the only
condition $\sup\limits_{t\in (0,r)}\dfrac{h(t)}{th'(t)}<+\infty$. This
condition is satisfied by any power functions $t\mapsto t^d$ of degree $d>0$.
The estimates are optimal in a certain sense.
