Note that the meaning of the exponent β in (19) changes for γ < 1 /z$_{c}$ and for γ > 1 /z$_{c}$ . For γ < 1 /z$_{c}$ this exponent describes the short time dependence of the spatially averaged pointwise width with time, as in the classical situation. For γ > 1 /z$_{c}$ , as we have mentioned, it describes the center of mass fluctuations, i. e., the less dominant source of fluctuations is chosen in each regime. For γ < 1 /z$_{c}$ and α > 0 (which implies the height difference correlation is well defined and the pointwise width is finite) there are always center of mass fluctuations. For γ > 1 /z$_{c}$ the situation is different as it is possible to find growth regimes with no center of mass fluctuations and which pointwise width increases as a power law of time. This is precisely the weak converge to the hyperspherical profile: while microscopically the interface is rough, macroscopically it is a concentrically propagating hypersphere. The change of meaning of the exponent β coincides with a change of physics. The long range shape of the interface is no longer affected by the diffusion mechanism, which becomes irrelevant, but for the system size evolution, which sculptures the resulting profile [20]. And so, the violation of scaling (2) is associated with the advent of a new dominant physical mechanism in the interface macroscale: system size growth overtakes diffusion and determines the cluster macroscopic shape. This work has been partially supported by the MICINN (Spain) through Project No. MTM2010-18128. Acknowledgments [1] D. W. Thompson, On Growth and Form (Cambridge University Press, Cambridge, 1917). [2] A. M. Turing, Phil. Trans. R. Soc. B 237 , 37 (1952). [3] M. Eden, in Symposium on Information Theory in Biology , edited by H. P. Yockey (Pergamon Press, New York, 1958). [4] M. Eden, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability , edited by J. Neyman (University of California Press, Berkeley, 1961). [5] C. A. Haselwandter and D. D. Vvedensky, Phys. Rev. Lett. 98 , 046102 (2007). [6] C. A. Haselwandter and D. D. Vvedensky, Phys. Rev. E 76 , 041115 (2007). 13