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The use of effective-one-body (EOB) waveforms for black hole binariesanalysis in gravitational-wave astronomy requires faithful models and fastgeneration times. A key aspect to achieve faithfulness is the inclusion ofnumerical-relativity (NR) informed next-to-quasicircular corrections(NQC),dependent on the radial momentum, to the waveform and radiation reaction. Arobust method to speed up the waveform generation is the post-adiabaticiteration to approximate the solution of the EOB Hamiltonian equations. In thiswork, we assess the performances of a fast NQC prescription in combination tothe post-adiabatic method for generating multipolar gravitational waves. Theoutlined approach allows a consistent treatment of NQC in both the waveform andthe radiation-reaction, does not require iterative procedures to achieve highfaithfulness, and can be efficiently employed for parameter estimation.Comparing to 611 NR simulations, for total mass $10M_\odot\leq M \leq200M_\odot$ and using the Advanded LIGO noise, the model has EOB/NRunfaithfulness well below $0.01$, with 78.5\% of the cases below $0.001$. Weapply the model to the parameter estimation of GW150914 exploring the impact ofthe new NQC and of the higher modes up to $\ell=m=8$.

TEOBResumS: assessment of consistent next-to-quasicircular corrections and post-adiabatic approximation in multipolar binary black holes waveforms