  We introduce a new model of preferential attachment with fitness, and
establish a time reversed duality between the model and a system of
branching-coalescing particles. Using this duality, we give a clear and concise
explanation for the condensation phenomenon, in which unusually fit vertices
may obtain abnormally high degree: it arises from a growth-extinction dichotomy
within the branching part of the dual. We show further that the condensation is
extensive. As the graph grows, unusually fit vertices become, each only for a
limited time, neighbouring to a non-vanishing proportion of the current graph.
