  We study the behavior of the two-dimensional two-component plasma in the
presence of some adsorbing impurities. Using a solvable model, we find analytic
expressions for the thermodynamic properties of the plasma such as the $n$-body
densities, the grand potential, and the pressure. We specialize in the case
where there are one or two adsorbing point impurities in the plasma, and in the
case where there are one or two parallel adsorbing lines. In the former case we
study the effective interaction between the impurities, due to the charge
redistribution around them. The latter case is a model for electrodes with
adsorbing sticky sites on their surface.
