The association between oppositely charged branched polyethylenimine (BPEI) and polymethacrylic acid (PMA) in the dilute regime is investigated using turbidimetric titration and electrophoretic mobility measurements. The complexation is controlled by tuning continuously the pH-sensitive charge of the polyacid in acidic solution. The formation of soluble and stable positively charged complexes is a cooperative process characterized by the existence of two regimes of weak and strong complexation. In the regime of weak complexation, a long PMA chain overcharged by several BPEI molecules forms a binary complex. As the charge of the polyacid increases, these binary complexes condense at a well defined charge ratio of the mixture to form large positively charged aggregates. The overcharging and the existence of two regimes of complexation are analyzed in the light of recent theories. The structure of the polyelectrolytes is investigated at higher polymer concentration by small angle neutron scattering. Binary complexes of finite size present an open structure where the polyacid chains connecting a small number of BPEI molecules have shrunk slightly. In the condensed complexes, BPEI molecules, wrapped by polyacid chains, form networks of stretched necklaces.