  We evaluate a strongly regularised version of the Hastings-Levitov model
HL$(\alpha)$ for $0\leq \alpha<2$. Previous results have concentrated on the
small-particle limit where the size of the attaching particle approaches zero
in the limit. However, we consider the case where we rescale the whole cluster
by its capacity before taking limits, whilst keeping the particle size fixed.
We first consider the case where $\alpha=0$ and show that under capacity
rescaling, the limiting structure of the cluster is not a disk, unlike in the
small-particle limit. Then we consider the case where $0<\alpha<2$ and show
that under the same rescaling the cluster approaches a disk. We also evaluate
the fluctuations and show that, when represented as a holomorphic function,
they behave like a Gaussian field dependent on $\alpha$. Furthermore, this
field becomes degenerate as $\alpha$ approaches 0 and 2, suggesting the
existence of phase transitions at these values.
