  We provide a general framework and indicate relations between the notions of
transfinite diameter, homogeneous transfinite diameter, and weighted
transfinite diameter for sets in C^N. An ingredient is a formula of Rumely
which relates the Robin function and the transfinite diameter of a compact set.
We also prove limiting formulas for integrals of generalized Vandermonde
determinants with varying weights for a general class of compact sets and
measures in C^N. Our results extend to certain weights and measures defined on
cones in R^N.
