  We continue the study in \cite{As18, AAZ18} by giving a multitude of
applications of projective logarithmic potentials. First we introduce the
notions of projective logarithmic energy and capacity associated to projective
kernel that was introduced and studied in \cite{As18, AAZ18}. We compare
quantitatively the projective logarithmic capacity with the complex
Monge-Amp\`ere capacity on $\mathbb P^n$ and we deduce that the set of zero
logarithmic capacity is of Monge-Amp\`ere capacity zero. Further, we define
transfinite diameter of a compact set and we show that it coincides with
logarithmic capacity. Finally we deduce that there is an analogous of classical
Evans's theorem that for any compact set $K$ of zero projective logarithmic
capacity shows the existence of Probability measure whose potential admits $K$
as polar set.
