  Patterns of animate and inanimate systems show remarkable similarities in
their aggregation. One similarity is the double-Pareto distribution of the
aggregate-size of system components. Different models have been developed to
predict aggregates of system components. However, not many models have been
developed to describe probabilistically the aggregate-size distribution of any
system regardless of the intrinsic and extrinsic drivers of the aggregation
process. Here we consider natural animate systems, from one of the greatest
mammals - the African elephant (\textit{Loxodonta africana}) - to the
\textit{Escherichia coli} bacteria, and natural inanimate systems in river
basins. Considering aggregates as islands and their perimeter as a curve
mirroring the sculpting network of the system, the probability of exceedence of
the drainage area, and the Hack's law are shown to be the the Kor\v{c}ak's law
and the perimeter-area relationship for river basins. The perimeter-area
relationship, and the probability of exceedence of the aggregate-size provide a
meaningful estimate of the same fractal dimension. Systems aggregate because of
the influence exerted by a physical or processes network within the system
domain. The aggregate-size distribution is accurately derived using the
null-method of box-counting on the occurrences of system components. The
importance of the aggregate-size spectrum relies on its ability to reveal
system form, function, and dynamics also as a function of other coupled
systems. Variations of the fractal dimension and of the aggregate-size
distribution are related to changes of systems that are meaningful to monitor
because potentially critical for these systems.
