How to determine if a random graph with a fixed degree sequence has a giant component

For a fixed degree sequence D=(d1,…,dn) , let G(D) be a uniformly chosen (simple) graph on {1,…,n} where the vertex i has degree di . In this paper we determine whether G(D) has a giant component with high probability, essentially imposing no conditions on D . We simply insist that the sum of the degrees in D which are not 2 is at least ¿(n) for some function ¿ going to infinity with n. This is a relatively minor technical condition, and when D does not satisfy it, both the probability that G(D) has a giant component and the probability that G(D) has no giant component are bounded away from 1Postprint (author's final draft