  We investigate irreversible aggregation in which monomer-monomer,
monomer-cluster, and cluster-cluster reactions occur with constant but distinct
rates K_{MM}, K_{MC}, and K_{CC}, respectively. The dynamics crucially depends
on the ratio gamma=K_{CC}/K_{MC} and secondarily on epsilon=K_{MM}/K_{MC}. For
epsilon=0 and gamma<2, there is conventional scaling in the long-time limit,
with a single mass scale that grows linearly in time. For gamma >= 2, there is
unusual behavior in which the concentration of clusters of mass k, c_k decays
as a stretched exponential in time within a boundary layer k<k* propto
t^{1-2/gamma} (k* propto ln t for gamma=2), while c_k propto t^{-2} in the bulk
region k>k*. When epsilon>0, analogous behaviors emerge for gamma<2 and gamma
>= 2.
