  We give a general formula for the $C-$transfinite diameter $\delta_C(K)$ of a
compact set $K\subset \mathbb{C}^2$ which is a product of univariate compacta
where $C\subset (\mathbb{R}^+)^2$ is a convex body. Along the way we prove a
Rumely type formula relating $\delta_C(K)$ and the $C-$Robin function
$\rho_{V_{C,K}}$ of the $C-$extremal plurisubharmonic function $V_{C,K}$ for $C
\subset (\mathbb{R}^+)^2$ a triangle $T_{a,b}$ with vertices $(0,0), (b,0),
(0,a)$. Finally, we show how the definition of $\delta_C(K)$ can be extended to
include many nonconvex bodies $C\subset \mathbb{R}^d$ for $d-$circled sets
$K\subset \mathbb{C}^d$, and we prove an integral formula for $\delta_C(K)$
which we use to compute a formula for the $C-$transfinite diameter of the
Euclidean unit ball $\mathbb{B}\subset \mathbb{C}^2$.
