  Radio galaxies are luminous structures created by the jets of supermassive
black holes, and consist of atomic nuclei, relativistic electrons, and magnetic
fields. In exceptional cases, radio galaxies attain cosmological, megaparsec
extents - and thus turn into giants. Giants embody the most extreme known
mechanism through which galaxies can impact the Cosmic Web around them. The
triggers of giant growth remain a mystery. Excitingly, new sensitive
low-frequency sky surveys hold promise to change this situation. In this work,
we perform a precision measurement of the distribution of giant growth's
central dynamical quantity: total length. We first construct a statistical
geometric framework for radio galaxies that is both rigorous and practical. We
then search the LOFAR Two-metre Sky Survey for giants, discovering 2060
previously unknown specimina: more than have been found in all preceding
literature combined. Spectacular discoveries include the longest giant hosted
by an elliptical galaxy, the longest giant hosted by a spiral galaxy, and 13
giants with an angular length larger than that of the full Moon. By combining
theory and observations - and carefully forward modelling selection effects -
we infer that giant radio galaxy lengths are well described by a Pareto
distribution with tail index $-3.5 \pm 0.5$. This finding is a new
observational constraint for models and simulations of radio galaxy growth. In
addition, for the first time, we determine the comoving number density of
giants, $5 \pm 2\ (100\ \mathrm{Mpc})^{-3}$, and the volume-filling fraction of
giant radio galaxy lobes in clusters and filaments, $5\substack{+8\\-2}\cdot
10^{-6}$. We conclude that giants are truly rare - not only from an
observational perspective, but also from a cosmological one. At any moment in
time, most clusters and filaments - the building blocks of the modern Cosmic
Web - do not harbour giants.
