Surface growth driven by nonmonomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P\left(s\right)\sim s^{-\tau }$. We find that the critical exponents vary continuously with $\tau$, recovering Kardar-Parisi-Zhang behavior only for $\tau \ge 3$. For $\tau <3$, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale $\zeta$, corresponding to the linear size of the largest cluster, in addition to the usual correlation length $\xi$. The coexistence of these two relevant scales signals the breakdown of the usual Family-Vicsek scaling. These results point to an interesting phenomenology of surface growth beyond the standard scale-invariant paradigm.

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• Growth processes
• Surface growth