  Gravitational-wave (GW) recoil of merging supermassive black holes (SMBHs)
may influence the co-evolution of SMBHs and their host galaxies. We examine
this possibility using SPH/N-body simulations of gaseous galaxy mergers in
which the merged BH receives a recoil kick. This enables us to follow recoiling
BHs in self-consistent, evolving merger remnants. In contrast to recent studies
on similar topics, we conduct a large parameter study, generating a suite of
over 200 simulations with more than 60 merger models and a range of recoil
velocities (vk). Our main results are as follows. (1) BHs kicked at nearly the
central escape speed (vesc) may oscillate on large orbits for up to a Hubble
time, but in gas-rich mergers, BHs kicked with up to ~ 0.7 vesc may be confined
to the central few kpc of the galaxy, owing to gas drag and steep central
potentials. (2) vesc in gas-rich mergers may increase rapidly during final
coalescence, in which case trajectories may depend on the timing of the BH
merger relative to the formation of the potential well. (3) Recoil events
generally reduce the lifetimes of bright active galactic nuclei (AGN), but may
actually extend AGN lifetimes at lower luminosities. (4) Kinematically-offset
AGN (v > 800 km s^-1) may be observable for up to ~ 10 Myr either immediately
after the recoil or during pericentric passages through a gas-rich remnant. (5)
Spatially-offset AGN (R > 1 kpc) generally have low luminosities and lifetimes
of ~ 1 - 100 Myr. (6) Rapidly-recoiling BHs may be up to ~ 5 times less massive
than their stationary counterparts. This lowers the normalization of the
M-sigma relation and contributes to both intrinsic and overall scatter. (7)
Finally, the displacement of AGN feedback after a recoil event enhances central
star formation rates, thereby extending the starburst phase of the merger and
creating a denser stellar cusp. [Abridged.]
