  The dynamics of fluctuating radially growing interfaces is approached using
the formalism of stochastic growth equations on growing domains. This framework
reveals a number of dynamic features arising during surface growth. For fast
growth, dilution, which spatially reorders the incoming matter, is responsible
for the transmission of correlations. Its effects include the erasing of memory
with respect to the initial condition, a partial attenuation of geometrically
originated instabilities, and the restoring of universality in some special
cases in which the critical exponents depend on the parameters of the equation
of motion. In this sense, dilution rends the dynamics more similar to the usual
one of planar systems. This fast growth regime is also characterized by the
spatial decorrelation of the interface, which in the case of radially growing
interfaces naturally originates rapid roughening and scale dependent
fractality, and suggests the advent of a self-similar fractal dimension. The
center of mass fluctuations of growing clusters are also studied, and our
analysis suggests the possible non-applicability of usual scalings to the long
range surface fluctuations of the radial Eden model. In fact, our study points
to the fact that this model belongs to a dilution-free universality class.
