  We consider a family of growth models defined using conformal maps in which
the local growth rate is determined by $|\Phi_n'|^{-\eta}$, where $\Phi_n$ is
the aggregate map for $n$ particles. We establish a scaling limit result in
which strong feedback in the growth rule leads to one-dimensional limits in the
form of straight slits. More precisely, we exhibit a phase transition in the
ancestral structure of the growing clusters: for $\eta>1$, aggregating
particles attach to their immediate predecessors with high probability, while
for $\eta<1$ almost surely this does not happen.
