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The interaction of polyacrylic acid stars with the number of arms N ((PAA)N, N = 5, 8, 21; DPn(arm) = 100) with strong linear cationic polyelectrolytes, viz., exhaustively quaternized poly-4-vinylpyridine (P4VPQ, DPw = 600) and exhaustively quaternized poly-2-vinylpyridine (P2VPQ, DPn = 42), in aqueous media (pH 7, 0.05 M ≤ [NaCl] ≤ 0.3 M) was examined. Mixing aqueous solutions of (PAA)N and P4VPQ or (PAA)N and P2VPQ was found to result in formation of homogeneous mixtures if the base-molar stoichiometry Z (Z = [N+]/[COO- + COOH] < 1) of such mixtures, does not exceed a certain threshold value Z*. The values of Z* were shown to become lower with decreasing the number of arms of (PAA)N as well as with increasing ionic strength in the mixtures of the oppositely charged polymeric components, being at the same time nearly independent of the chain length of the linear cationic polyelectrolyte. In the case of (PAA)N interacting with P4VPQ, the formed homogeneous mixtures of the oppositely charged polymeric components (Z < Z*) were found to contain typically two types of the scattering complex species, the hydrodynamic size of the small complex species (Rh = 8 ÷ 15 nm) being comparable with that measured for the corresponding macromolecules of (PAA)N whereas the hydrodynamic size of the large complex species (Rh = 55 ÷ 90 nm) considerably exceeding that determined for the corresponding macromolecules of (PAA)N. The increase of the base-molar stoichiometry of such mixtures as well as the increase of their ionic strength was demonstrated to result in the increasing fraction of large complex species while the hydrodynamic sizes of both large and small complex species remain nearly constant. Static light scattering measurements carried out under conditions when the scattering contribution of the small complex species is negligible (N = 5, Z = 0.2, pH 7, 0.1 M NaCl) provide evidence that the large complex species have rather high molecular weight (Mw = 8E+06 g/mole) and relatively compact (Rg = 75 nm, Rg/Rh = 1). Such large complex species might be considered as precursors of insoluble interpolyelectrolyte complexes formed in the mixtures of (PAA)N and P4VPQ at Z > Z*. In the case of (PAA)N interacting with P2VPQ, the formed homogeneous mixtures of the oppositely charged polymeric components (Z < Z*) were also found to contain two types of the scattering complex species but the fraction of the large complex species appears to be extremely small. The hydrodynamic size of the small complex species (Rh = 8 ÷ 15 nm) was measured to be very close to that determined for the corresponding macromolecules of (PAA)N. Static light scattering measurements (N = 21, Z = 0.2, pH 7, 0.1 M NaCl) provide evidence that molecular weight of the small complex species (Mw = 2.9E+05 g/mole) is comparable with molecular weight calculated theoretically under assumption that their base-molar stoichiometry coincides with the base-molar stoichiometry of the mixture of (PAA)21 and P2VPQ (Mn(theor) = 2.5E+05 g/mole). Such small species are considered as particles of water-soluble interpolyelectrolyte complex, each comprising only one macromolecule of (PAA)N and such the number of P2VPQ chains which corresponds to their base-molar stoichiometry ɸ = Z.