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The interaction of star-shaped poly(acrylic acid) ((PAA)N) having various numbers of arms, N = 5, 8, 21, DPn(arm) = 100) with exhaustively quaternized poly(4-vinylpyridine) (P4VPQ, DPn = 290, quaternized with ethyl bromide) and exhaustively quaternized poly(2-vinylpyridine)s (P2VPQ, DPn = 40 - 430, quaternized with dimethyl sulfate) was examined in aqueous media (pH 7) by means of turbidimetry, dynamic and static light scattering, and analytical ultracentrifugation. Mixing aqueous solutions of the oppositely charged polymeric components was found to result in appearance of turbidity only if their base-molar stoichiometry Z (Z = [N+]/[COO- + COOH] < 1) exceeds a certain threshold value ZM, that is, the aqueous mixtures of (PAA)N and P4(2)VPQ were transparent at Z < ZM, thereby strongly suggesting the formation of water-soluble interpolyelectrolyte complexes (IPECs), whereas they underwent phase separation at Z > ZM, thus indicating the formation of insoluble IPECs. At Z < ZM, the homogeneous aqueous mixtures of (PAA)N and P4(2)VPQ were found to contain two types of complex species clearly differing in their sizes, hydrodynamic radii of the small complex species being close to those measured for the corresponding (PAA)N whle hydrodynamic radii of the large complex species considerably exceeding those determined for the corresponding (PAA)N. The fractions of thes macromolecular co-assemblies were shown to be dependent on N, DPn of the linear cationic polyelectrolyte, Z, and the ionic strength of the surrounding solution. The small complex species (dominant fraction) are assumed to represent the particles of the water-soluble IPECs in which (PAA)N plays a role of lyophilizing polymeric component. Each particle of such water-soluble IPEC is considered to have the "core-corona" structure with a hydrophobic core assembled from fragments of the oppositely charged polymeric components and a hydrophilic corona built up from the arms (or fragments of the arms) of (PAA)N which are not coupled to P4(2)VPQ. The large complex species having high molecular weight and being rather compact are thought to be complex aggregates which represent peculiar precursors of insoluble IPECs formed upon a further increasing content of P4(2)VPQ in the aqueous mixtures of the oppositely charged polymeric components.