We report results on studies of the e+e- annihilation into three-body Y(nS)pi+pi- (n=1,2,3) final states including measurements of cross sections and the full amplitude analysis. The cross sections measured at sqrt(s)=10.865 GeV and corrected for the initial state radiation are sigma(e+e-=>Y(1S)pi+pi-)=(2.27±0.12±0.14) pb, sigma(e+e-=>Y(2S)pi+pi-)=(4.07±0.16±0.45) pb, and sigma(e+e-=>Y(3S)pi+pi-)=(1.46±0.09±0.16) pb. Amplitude analysis of the three-body Y(nS)pi+pi- final states strongly favors I^G(J^P)=1^+(1^+) quantum-number assignments for the two bottomonium-like Zb± states, recently observed in the Y(nS)pi± and hb(mP)pi± (m=1,2) decay channels. The results are obtained with a $121.4 1/fb data sample collected with the Belle detector at the KEKB asymmetric-energy e+e- collider.

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