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We consider the tributary structure of Howard's drainage model studied byGangopadhyay et. al. Conditional on the event that the tributary survives up totime $n$, we show that, as a sequence of random metric spaces, scaled tributaryconverges in distribution to a continuum random tree with respect to GromovHausdorff topology. This verifies a prediction made by Aldous for a simplermodel (where paths are independent till they coalesce) but for a differentconditional set up. The limiting continuum tree is slightly different from whatwas surmised earlier. Our proof uses the fact that there exists a dual processsuch that the original network and it's dual jointly converge in distributionto the Brownian web and it's dual.

Continuum random tree as the scaling limit for a drainage network model: a Brownian web approach