Throughout this chapter we consider the Coulomb gas model ( 1.12 ) with general \(\beta > 0\) , for which we use the notation OCP, which stands for one-component plasma. The special case \(\beta = 2\) coincides with GinUE. The study of thermodynamic properties of the OCP requires the asymptotic expansion of the logarithm of the renormalised configuration integral for large N. This holds true for the Coulomb gas model confined to general domains. A conjectured universal logarithmic term, which is proportional to the Euler characteristic of the domain, is highlighted and a conjecture for the \(\sqrt{N}\) surface tension term in the case of disk geometry is also reported, as are some exact results for the energy per particle. In relation to the edge-scaled charge density, sum rules for the total charge and the dipole moment are given, and an asymptotic expansion of the density outside of the droplet is formulated, which as the multiplicative constant term involves the dimensionless free energy per particle. The final section of the chapter addresses sum rules and asymptotics associated with the truncated two-point correlation function, which is conveniently interpreted as the screening cloud about a fixed charge. Its Fourier transform gives the structure function, for which several terms in the small wavenumber expansion can be predicted. Also emphasised is distinct, slowly decaying, asymptotic behaviour of the truncated two-point correlation function at the boundary.