  In this work, we study the long time asymptotics of a coagulation model which
describes the evolution of a system of particles characterized by their volume
and surface area. The aggregation mechanism takes place in two stages:
collision and fusion of particles. During the collision stage, the two
particles merge at a contact point. The newly formed particle has volume and
area equal to the sum of the respective quantities of the two colliding
particles. After collision, the fusion phase begins and during it the geometry
of the interacting particles is modified in such a way that the volume of the
total system is preserved and the surface area is reduced. During their
evolution, the particles must satisfy the isoperimetric inequality. Therefore,
the distribution of particles in the volume and area space is supported in the
region where $\{a\geq (36\pi)^{\frac{1}{3}}v^{\frac{2}{3}}\}$. We assume the
coagulation kernel has a weak dependence on the area variable. We prove
existence of self-similar profiles for some choices of the functions describing
the fusion rate for which the particles have a shape that is close to
spherical. On the other hand, for other fusion mechanisms and suitable choices
of initial data, we show that the particle distribution describes a system of
ramified-like particles.
