  A dimensionless parameter $\Lambda$ is proposed to describe a hierarchy of
morphologies in two-dimensional (2D) aggregates formed due to varying
competition between short-range attraction and long-range repul- sion.
Structural transitions from finite non-compact to compact to percolated
structures are observed in the configurations simulated by molecular dynamics
at a constant temperature and density. Configurational randomness across the
transition, measured by the two-body excess entropy $S_2$, exhibits data
collapse with the average potential energy $\bar{\mathcal{E}}$ of the systems.
Independent master curves are presented among $S_2$, the reduced second virial
coefficient $B_2^*$ and $\Lambda$, justifying this minimal description. This
work lays out a coherent basis for the study of 2D aggregate morphologies
relevant to diverse nano- and bio-processes.
