  The homogeneous partly pinned fluid systems are simple models of a fluid
confined in a disordered porous matrix obtained by arresting randomly chosen
particles in a one-component bulk fluid or one of the two components of a
binary mixture. In this paper, their configurational properties are
investigated. It is shown that a peculiar complementarity exists between the
mobile and immobile phases, which originates from the fact that the solid is
prepared in presence of and in equilibrium with the adsorbed fluid. Simple
identities follow, which connect different types of configurational averages,
either relative to the fluid-matrix system or to the bulk fluid from which it
is prepared. Crucial simplifications result for the computation of important
structural quantities, both in computer simulations and in theoretical
approaches. Finally, possible applications of the model in the field of
dynamics in confinement or in strongly asymmetric mixtures are suggested.
