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We establish some scaling limits for a model of planar aggregation. The modelis described by the composition of a sequence of independent and identicallydistributed random conformal maps, each corresponding to the addition of oneparticle. We study the limit of small particle size and rapid aggregation. Theprocess of growing clusters converges, in the sense of Caratheodory, to aninflating disc. A more refined analysis reveals, within the cluster, a treestructure of branching fingers, whose radial component increasesdeterministically with time. The arguments of any finite sample of fingers,tracked inwards, perform coalescing Brownian motions. The arguments of anyfinite sample of gaps between the fingers, tracked outwards, also performcoalescing Brownian motions. These properties are closely related to theevolution of harmonic measure on the boundary of the cluster, which is shown toconverge to the Brownian web.

Hastings-Levitov aggregation in the small-particle limit