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We study competition on scale-free random graphs, where the degreedistribution satisfies an asymptotic power-law with infinite variance. Ourcompetition process is such that the two types attempt at occupying verticesincident to the presently occupied sets, and the passage times are independentand identically distributed, possibly with different distributions for the twotypes. Once vertices are occupied by a type, they remain on being so.  We focus on the explosive setting, where our main result shows that thewinning type occupies all but a finite number of vertices. This universal`winner-takes-it-all' phenomenon significantly generalises previous work withDeijfen for exponential edge-weights, and considerably simplifies its proof.

Universal `winner-takes-it-all' phenomenon in scale-free random graphs