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We present measurements of the branching fractions and charge asymmetries (where appropriate) of two-body B decays to eta(('))K(*), eta(('))rho, eta(('))pi(0), omegapi(0), and phipi(0). The data were recorded with the BABAR detector at PEP-II and correspond to 89x10(6) B (B) over bar pairs produced in e(+)e(-) annihilation through the Y(4S) resonance. We find significant signals for two decay modes and measure the branching fractions B(B+-->etaK(*+))=(25.6+/-4.0+/-2.4)x10(-6) and B(B-0-->etaK(*0))=(18.6+/-2.3+/-1.2)x10(-6), where the first error is statistical and the second systematic. We also find evidence with significance 3.5sigma for a third decay mode and measure B(B+-->etarho(+))=(9.2+/-3.4+/-1.0)x10(-6). For other channels, we set 90% C.L. upper limits of B(B-0-->etarho(0))<1.5x10(-6), B(B+-->eta(')K(*+))<14x10(-6), B(B-0-->eta(')K(*0))<7.6x10(-6), B(B+-->eta(')rho(+))<22x10(-6), B(B-0-->eta(')rho(0))<4.3x10(-6), B(B-0-->etapi(0))<2.5x10(-6), B(B-0-->eta(')pi(0))<3.7x10(-6), B(B-0-->omegapi(0))<1.2x10(-6), and B(B-0-->phipi(0))<1.0x10(-6). For self-flavor-tagging modes with significant signals, the time-integrated charge asymmetries are A(ch)(etaK(*+))=+0.13+/-0.14+/-0.02 and A(ch)(etaK(*0))=+0.02+/-0.11+/-0.02

B meson decays to η(′)K*, η(′)ρ, η(′)π0, ωπ0, and φπ0