  We study the nonequilibrium phase transition in a model of aggregation of
masses allowing for diffusion, aggregation on contact and fragmentation. The
model undergoes a dynamical phase transition in all dimensions. The steady
state mass distribution decays exponentially for large mass in one phase. On
the contrary, in the other phase it has a power law tail and in addition an
infinite aggregate. The model is solved exactly within a mean field
approximation which keeps track of the distribution of masses. In one
dimension, by mapping to an equivalent lattice gas model, exact steady states
are obtained in two extreme limits of the parameter space. Critical exponents
and the phase diagram are obtained numerically in one dimension. We also study
the time dependent fluctuations in an equivalent interface model in (1+1)
dimension and compute the roughness exponent $\chi$ and the dynamical exponent
z analytically in some limits and numerically otherwise. Two new fixed points
of interface fluctuations in (1+1) dimension are identified. We also generalize
our model to include arbitrary fragmentation kernels and solve the steady
states exactly for some special choices of these kernels via mappings to other
solvable models of statistical mechanics.
