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Based on the method of collective variables (CV) with a reference system, the exact expression for the functional of the grand partition function of a m-component ionic model with charge and size asymmetry is found. Particular attention is paid to the nth particle correlation functions of the reference system which is presented as a m-component system of "colour" hard spheres of the same diameter. A two-component model is considered in more detail. In this case the recurrence formulas for thedoi:10.5488/cmp.9.4.659 fatcat:cn5kxt2uhvdkpnrypiggwnn4qi