  A diffusion-limited aggregation process, in which clusters coalesce by means
of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a
heuristic argument that predicts logarithmic corrections to the mean-field
asymptotic behavior for the concentration of clusters of mass $m$ at time $t$,
$c(m,t)~m^{-1/2}(log(t)/t)^{3/4}$, for $1 << m << \sqrt{t/log(t)}$. The total
concentration of clusters, $c(t)$, decays as $c(t)~\sqrt{log(t)/t}$ at $t -->
\infty$. We also investigate the problem with a localized steady source of
monomers and find that the steady-state concentration $c(r)$ scales as
$r^{-1}(log(r))^{1/2}$, $r^{-1}$, and $r^{-1}(log(r))^{-1/2}$, respectively,
for the spatial dimension $d$ equal to 1, 2, and 3. The total number of
clusters, $N(t)$, grows with time as $(log(t))^{3/2}$, $t^{1/2}$, and
$t(log(t))^{-1/2}$ for $d$ = 1, 2, and 3. Furthermore, in three dimensions we
obtain an asymptotic solution for the steady state cluster-mass distribution:
$c(m,r) \sim r^{-1}(log(r))^{-1}\Phi(z)$, with the scaling function
$\Phi(z)=z^{-1/2}\exp(-z)$ and the scaling variable $z ~ m/\sqrt{log(r)}$.

Condensed Matter