  Over the course of the third observing run of LIGO-Virgo-KAGRA Collaboration,
several gravitational-wave (GW) neutron star--black hole (NSBH) candidates have
been announced. By assuming these candidates are real signals and of
astrophysical origins, we analyze the population properties of the mass and
spin distributions for GW NSBH mergers. We find that the primary BH mass
distribution of NSBH systems, whose shape is consistent with that inferred from
the GW binary BH (BBH) primaries, can be well described as a power-law with an
index of $\alpha = 4.8^{+4.5}_{-2.8}$ plus a high-mass Gaussian component
peaking at $\sim33^{+14}_{-9}\,M_\odot$. The NS mass spectrum could be shaped
as a near flat distribution between $\sim1.0-2.1\,M_\odot$. The constrained NS
maximum mass agrees with that inferred from NSs in our Galaxy. If GW190814 and
GW200210 are NSBH mergers, the posterior results of the NS maximum mass would
be always larger than $\sim2.5\,M_\odot$ and significantly deviate from that
inferred in the Galactic NSs. The effective inspiral spin and effective
precession spin of GW NSBH mergers are measured to potentially have near-zero
distributions. The negligible spins for GW NSBH mergers imply that most events
in the universe should be plunging events, which supports the standard isolated
formation channel of NSBH binaries. More NSBH mergers to be discovered in the
fourth observing run would help to more precisely model the population
properties of cosmological NSBH mergers.
