ω* has (almost) no continuous images

We prove that the following statement follows from the Open Colouring Axiom (OCA): if X is locally compact sigma-compact but not compact and if its Cech-Stone remainder X* is a continuous image of omega*, then X is the union of omega and a compact set. It follows that the remainders of familiar spaces like the real line or the sum of countably many Canter sets need not be continuous images of omega*.