  We calculate exactly the two point mass-mass correlations in arbitrary
spatial dimensions in the aggregation model of Takayasu. In this model, masses
diffuse on a lattice, coalesce upon contact and adsorb unit mass from outside
at a constant rate. Our exact calculation of the variance of mass at a given
site proves explicitly, without making any assumption of scaling, that the
upper critical dimension of the model is 2. We also extend our method to
calculate the spatio-temporal correlations in a generalized class of models
with aggregation, fragmentation and injection which include, in particular, the
$q$-model of force fluctuations in bead packs. We present explicit expressions
for the spatio-temporal force-force correlation function in the $q$-model.
These can be used to test the applicability of the $q$-model in experiments.
