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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.