  The Laplacian Growth (LG) model is known as a universality class of
scale-free aggregation models in two dimensions, characterized by classical
integrability and featuring finite-time boundary singularity formation. A
discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar
local growth law, but significantly different global behavior. For both LG and
DLA, a proper description for the scaling properties of long-time solutions is
not available yet. In this note, we outline a possible approach towards finding
the correct theory yielding a regularized LG and its relation to DLA.
