  We present a detailed investigation into the properties of GW170729, the
gravitational wave with the most massive and distant source confirmed to date.
We employ an extensive set of waveform models, including new improved models
that incorporate the effect of higher-order waveform modes which are
particularly important for massive systems. We find no indication of
spin-precession, but the inclusion of higher-order modes in the models results
in an improved estimate for the mass ratio of $(0.3-0.8)$ at the 90\% credible
level. Our updated measurement excludes equal masses at that level. We also
find that models with higher-order modes lead to the data being more consistent
with a smaller effective spin, with the probability that the effective spin is
greater than zero being reduced from $99\%$ to $94\%$. The 90\% credible
interval for the effective spin parameter is now $(-0.01-0.50)$. Additionally,
the recovered signal-to-noise ratio increases by $\sim0.3$ units compared to
analyses without higher-order modes. We study the effect of common spin priors
on the derived spin and mass measurements, and observe small shifts in the
spins, while the masses remain unaffected. We argue that our conclusions are
robust against systematic errors in the waveform models. We also compare the
above waveform-based analysis which employs compact-binary waveform models to a
more flexible wavelet- and chirplet-based analysis. We find consistency between
the two, with overlaps of $\sim 0.9$, typical of what is expected from
simulations of signals similar to GW170729, confirming that the data are
well-described by the existing waveform models. Finally, we study the
possibility that the primary component of GW170729 was the remnant of a past
merger of two black holes and find this scenario to be indistinguishable from
the standard formation scenario.
