Size effects and scaling properties of statistical fractures represent an unsolved problem despite two decades of research activities. Many controversial issues exist between theoretical and experimental values, and among theoretical and numerical models, arising from the dependence of the strength on the characteristic lengthscales of the samples, rooted in the incorporated disorder. To describe the distribution of fracture strength the key theoretical tool is the extreme value statistics. Two models especially account for size effects in failure models: the weakest link model assumes that the failure strength of an object is ruled by its weakest subvolume and yields the Weibull distribution, while the largest crack model schematizes the material as a set of independent cracks with different lenghts and is ruled by the generalized Gumbel distribution. Such modelizations are investigated by discrete lattice models in which the elastic medium is described by a network of discrete elements. We adopt the Random Fuse Model (RFM), whose bonds are fuses connected to a voltage difference. In the diluted disorder RFM, a fraction of the bonds (all having the same conductance and breaking thresholds) is randomly removed and a voltage difference is applied between the top and bottom of the lattice. At every step the currents through the bonds are calculated and the bond traversed by the largest current is removed, until failure.This is an HPC problem due to the nature of the underlying statistics. Numerical simulations on very large system sizes are essential to understand the scaling laws of fracture and one needs an ensemble averaging of the numerical results over a large set of configurations to obtain a realistic representation of the system response. This tasks become severe with increasing system size and are approachables only thanks to supercomputing resources. The simulations performed in the frame of HPC-Europa2 project allowed an exhaustive characterization of the model, boosting both system sizes and statistical accuracy over previous results in the field. We simulated systems with different (square and diamond-like) topology and we investigated size- and scaling-effects through the analysis of the stress failure probability distribution. We found that it is not possible, unlike often assumed, to state an equivalence between V1 (the voltage at first bond-breaking) and Vf (the failure voltage). Results show that for large disordered systems the interactions between microcracks are negligible and the validity of extremal theory is recovered; data analysis confirms that the failure probability of a system of size L is related to the product of the probabilities of subsystems of size L/2 as expected by the theory. We compare Gumbel and Weibull distributions and show that the data are well described by the first one. We also show invariance between diamond-like and square systems.