  As a follow-up study of our previous work, numerical-relativity simulations
for seconds-long black hole-neutron star mergers are performed for a variety of
setups. Irrespective of the initial and symmetry conditions, we find
qualitatively universal evolution processes: The dynamical mass ejection takes
place together with a massive accretion disk formation after the neutron star
is tidally disrupted; Subsequently, the magnetic field in the accretion disk is
amplified by the magnetic winding, Kelvin-Helmholtz instability, and
magnetorotational instability, which establish a turbulent state inducing the
dynamo and angular momentum transport; The post-merger mass ejection by the
effective viscous processes stemming from the magnetohydrodynamics turbulence
sets in at $\sim300$-$500$ ms after the merger and continues for several
hundred ms; A magnetosphere near the black-hole spin axis is developed and the
collimated strong Poynting flux is generated with its lifetime of $\sim0.5$-$2$
s. We have newly found that the model of no equatorial-plane symmetry shows the
reverse of the magnetic-field polarity in the magnetosphere, which is caused by
the dynamo associated with the magnetorotational instability in the accretion
disk. The model with initially toroidal fields shows the tilt of the disk and
magnetosphere in the late post-merger stage because of the anisotropic
post-merger mass ejection. These effects could terminate the strong
Poynting-luminosity stage within the timescale of $\sim0.5$-$2$ s.
