the last inequality. This last inequality could be considered as desirable but correlation (17) has a different drawback. As we have said, the exponent β$_{r}$ describes the time power law dependence of the standard deviation of the interface center of mass position. For the Eden model, which in planar format belongs to the KPZ universality class [7], d = γ = 1 and so β$_{r}$ = 1 / 6. This exponent however does not agree with the one measured in simulations [25] and this constitutes another disadvantage of the use of scaling (2) in radial systems. We note that considering the planar KPZ equation on a growing domain does not simplify much things with respect to considering the full radial case [26]. Together with the KPZ equation, the Villain-Lai-Das Sarma (VLDS) equation [27, 28] is one of most important nonlinear models for surface growth. If one derives the VLDS equation in the radial setting one finds irrelevance of the diffusion for γ > 1 / 4 and of the nonlinearity for γ > 1 /z$_{c}$ . In this case the well known hyperscaling relation for conserved growth models yields 2 β$_{c}$ + d/z$_{c}$ = 1, and so equality of (17) with (11). This suggests that the scaling properties derived herein for linear models are also valid for some nonlinear models as the VLDS equation. In this work we have examined the dynamic scaling of radial interfaces. We have shown that long range fluctuations, which are describable by two-point correlation functions, be- come scale invariant for values of the critical exponents which may totally differ from the corresponding ones in a planar geometry. In rapidly growing radial systems we have found all of which have a clear physical meaning. The β$_{r}$ exponent, as we have discussed, describes the interface center of mass fluctuations. The α exponent associated to the radial surface fluctuation indicates how much the growing cluster deviates from a d − dimensional growing hypersphere. For α < 0 the growing cluster converges to a hypersphere concentrically growing at the deterministic rate t $^{γ}$, and in this sense the growth profile is flat. This sort of convergence is of course weak : the profile converges to the hypersphere on (any type of spatial) average. The microscopic roughness, which is given by the height-difference correlation, reduces to that of the planar profile [20] and precludes strong or pointwise α = 1 2 γ − d 2 , z = 1 γ , β$_{r}$ = 1 2 − γd 2 , (18) VI. CONCLUSIONS 11