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We consider a model of planar random aggregation from the ALE$(0,\eta)$family where particles are attached preferentially in areas of low harmonicmeasure. We find that the model undergoes a phase transition in negative$\eta$, where for sufficiently large values the attachment distribution of eachparticle becomes atomic in the small particle limit, with each particleattaching to one of the two points at the base of the previous particle. Thiscomplements the result of Sola, Turner and Viklund for large positive $\eta$,where the attachment distribution condenses to a single atom at the tip of theprevious particle.  As a result of this condensation of the attachment distributions we deducethat in the limit as the particle size tends to zero the ALE cluster convergesto a Schramm--Loewner evolution with parameter $\kappa = 4$ (SLE$_4$).  We also conjecture that using other particle shapes from a certain family, wehave a similar SLE scaling result, and can obtain SLE$_\kappa$ for any $\kappa\geq 4$.

SLE scaling limits for a Laplacian random growth model