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