Aggregation and fragmentation of single molecules  in the cell environment
lead  to statistical laws of movement different from Brownian motion. Employing
a many body approach, we  elucidate how the widely observed exponential tails
in the particle spreading, i.e. the Laplace distribution and the modulations of the
diffusivities, are controlled by size fluctuations of single molecules and for
different dependencies of the diffusion on the size of particles. By means of
numerical simulations Laplace distributions are obtained whether we track one
molecule or many molecules in parallel. Using a renewal process in the space of
sizes, we quantify to what extent the diffusivity varies significantly depending on
which tracking protocol is applied.