  We present a study of the scaling properties of cluster-cluster aggregation
with a source of monomers in the stationary state when the spatial transport of
particles occurs by Levy flights. We show that the transition from mean-field
statistics to fluctuation-dominated statistics which, for the more commonly
considered case of diffusive transport, occurs as the spatial dimension of the
system is tuned through two from above, can be mimicked even in one dimension
by varying the characteristic exponent, beta, of the the Levy jump length
distribution. We also show that the two-point mass correlation function,
responsible for the flux of mass in the stationary state, is strongly
universal: its scaling exponent is given by the mean field value independent of
the spatial dimension and independent of the value of beta. Finally we study
numerically the two point spatial correlation function which characterises the
structure of the depletion zone around heavy particles in the diffusion limited
regime. We find that this correlation function vanishes with a non-trivial
fractional power of the separation between particles as this separation goes to
zero. We provide a scaling argument for the value of this exponent which is in
reasonable agreement with the numerical measurements.
