Not yet reviewed by Pith; the record is open.

The no-hair conjecture in General Relativity (GR) states that a Kerr black hole (BH) is completely described by its mass and spin. As a consequence, the complex quasi-normal-mode (QNM) frequencies of a binary-black-hole (BBH) ringdown can be uniquely determined by the mass and spin of the remnant object. Conversely, measurement of the QNM frequencies could be an independent test of the no-hair conjecture. This paper extends to spinning BHs earlier work that proposed to test the no-hair conjecture by measuring the complex QNM frequencies of a BBH ringdown using parameterized inspiral-merger-ringdown waveforms in the effective-one-body formalism, thereby taking full advantage of the entire signal power and removing dependency on the predicted or estimated start time of the ringdown. Our method was used to analyze the properties of the merger remnants for BBHs observed by LIGO-Virgo in the first half of their third observing (O3a) run. After testing our method with GR and non-GR synthetic-signal injections in Gaussian noise, we analyze, for the first time, two BBHs from the first (O1) and second (O2) LIGO-Virgo observing runs, and two additional BBHs from the O3a run. We then provide joint constraints with published results from the O3a run. In the most agnostic and conservative scenario where we combine the information from different events using a hierarchical approach, we obtain, at $90\%$ credibility, that the fractional deviations in the frequency (damping time) of the dominant QNM are $\delta f_{220}=0.03^{+0.10}_{-0.09}$ ($\delta \tau_{220}=0.10^{+0.44}_{-0.39}$), respectively, an improvement of a factor of $\sim 4$ ($\sim 2$) over the results obtained with our model in the LIGO-Virgo publication. The single-event most-stringent constraint to date continues to be GW150914 for which we obtain $\delta f_{220}=0.05^{+0.11}_{-0.07}$ and $\delta \tau_{220}=0.07^{+0.26}_{-0.23}$.