  To check the dual superconductor picture for the quark-confinement mechanism,
we evaluate monopole dominance as well as Abelian dominance of quark
confinement for both quark-antiquark and three-quark systems in SU(3) quenched
lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian
dominance for the static $Q\bar Q$ system in lattice QCD with various spacing
$a$ at $\beta$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume
lattices with $La \ge$ 2fm, we find perfect Abelian dominance of the string
tension for the $Q\bar Q$ systems: $\sigma_{Abel} \simeq \sigma$. Second, we
accurately measure the static 3Q potential for more than 300 different patterns
of 3Q systems with 1000-2000 gauge configurations using two large
physical-volume lattices: ($\beta$,$L^3$x$L_t$)=(5.8,$16^3$x32) and
(6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be
well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type
linear term $\sigma L_{min}$, where $L_{min}$ is the minimum flux-tube length
connecting the three quarks. We find perfect Abelian dominance of the string
tension also for the 3Q systems: $\sigma^{Abel}_{3Q}\simeq \sigma_{3Q} \simeq
\sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice
QCD at $\beta$=5.8 on $16^3$x32 with 2,000 gauge configurations.
Abelian-projected QCD in the MA gauge has not only the color-electric current
$j^\mu$ but also the color-magnetic monopole current $k^\mu$, which
topologically appears. By the Hodge decomposition, the Abelian-projected QCD
system can be divided into the monopole part ($k_\mu \ne 0$, $j_\mu=0$) and the
photon part ($j_\mu \ne 0$, $k_\mu=0$). We find monopole dominance of the
string tension for $Q\bar Q$ and 3Q systems: $\sigma_{Mo}\simeq 0.92\sigma$.
While the photon part has almost no confining force, the monopole part almost
keeps the confining force.
