  The vapor-liquid critical behavior of intrinsically asymmetric fluids is
studied in finite systems of linear dimensions, $L$, focusing on periodic
boundary conditions, as appropriate for simulations. The recently propounded
``complete'' thermodynamic $(L\to\infty)$ scaling theory incorporating pressure
mixing in the scaling fields as well as corrections to scaling
${[arXiv:cond-mat/0212145]}$, is extended to finite $L$, initially in a grand
canonical representation. The theory allows for a Yang-Yang anomaly in which,
when $L\to\infty$, the second temperature derivative,
$(d^{2}\mu_{\sigma}/dT^{2})$, of the chemical potential along the phase
boundary, $\mu_{\sigma}(T)$, diverges when $T\to\Tc -$. The finite-size
behavior of various special {\em critical loci} in the temperature-density or
$(T,\rho)$ plane, in particular, the $k$-inflection susceptibility loci and the
$Q$-maximal loci -- derived from $Q_{L}(T,<\rho>_{L}) \equiv < m^{2}>^{2}_{L}/<
m^{4}>_{L}$ where $m \equiv \rho - <\rho>_{L}$ -- is carefully elucidated and
shown to be of value in estimating $\Tc$ and $\rhoc$. Concrete illustrations
are presented for the hard-core square-well fluid and for the restricted
primitive model electrolyte including an estimate of the correlation exponent
$\nu$ that confirms Ising-type character. The treatment is extended to the
canonical representation where further complications appear.
