  Many complex systems have been shown to share universal properties of
organization, such as scale independence, modularity and self-similarity. We
borrow tools from statistical physics in order to study structural preferential
attachment (SPA), a recently proposed growth principle for the emergence of the
aforementioned properties. We study the corresponding stochastic process in
terms of its time evolution, its asymptotic behavior and the scaling properties
of its statistical steady state. Moreover, approximations are introduced to
facilitate the modelling of real systems, mainly complex networks, using SPA.
Finally, we investigate a particular behavior observed in the stochastic
process, the peloton dynamics, and show how it predicts some features of real
growing systems using prose samples as an example.
