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We consider the statistical properties of arrival times and balls onfirst-passage percolation (FPP) $2D$ square lattices with strong disorder inthe link-times. A previous work showed a crossover in the weak disorder regime,between Gaussian and Kardar-Parisi-Zhang (KPZ) universality, with the crossoverlength decreasing as the noise amplitude grows. On the other hand, this workpresents a very different behavior in the strong-disorder regime. A newcrossover length appears below which the model is described by bond-percolationuniversality class. This characteristic length scale grows with the noiseamplitude and diverges at the infinite-disorder limit. We provide a thoroughcharacterization of the bond-percolation phase, reproducing its associatedcritical exponents through a careful scaling analysis of the balls. This iscarried out through to a continuous mapping of the FPP passage time into theoccupation probability of the bond-percolation problem. Moreover, the crossoverlength can be explained merely in terms of properties of the link-timedistribution. The interplay between the new characteristic length and thecorrelation length intrinsic to bond-percolation determines the crossoverbetween the initial percolation-like growth and theasymptotic KPZ scaling.

First-Passage Percolation under extreme disorder: from bond-percolation to Kardar-Parisi-Zhang universality