  In contrast to the water-poor inner solar system planets, stochasticity
during planetary formation and order of magnitude deviations in exoplanet
volatile contents suggest that rocky worlds engulfed in thick volatile ice
layers are the dominant family of terrestrial analogues among the extrasolar
planet population. However, the distribution of compositionally Earth-like
planets remains insufficiently constrained, and it is not clear whether the
solar system is a statistical outlier or can be explained by more general
planetary formation processes. Here we employ numerical models of planet
formation, evolution, and interior structure, to show that a planet's bulk
water fraction and radius are anti-correlated with initial $^{26}$Al levels in
the planetesimal-based accretion framework. The heat generated by this
short-lived radionuclide rapidly dehydrates planetesimals prior to accretion
onto larger protoplanets and yields a system-wide correlation of planet bulk
abundances, which, for instance, can explain the lack of a clear orbital trend
in the water budgets of the TRAPPIST-1 planets. Qualitatively, our models
suggest two main scenarios of planetary systems' formation: high-$^{26}$Al
systems, like our solar system, form small, water-depleted planets, whereas
those devoid of $^{26}$Al predominantly form ocean worlds, where the mean
planet radii between both scenarios deviate by up to about 10%.
