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We explore three sets of cosmological hydrodynamical simulations,IllustrisTNG, EAGLE, and SIMBA, to investigate the physical processes impactingthe distribution of baryons in and around haloes across an unprecedented massrange of $10^8<M_{\rm 200c}/{\rm M_{\odot}}<10^{15}$, from the halo centre outto scales as large as $30\,R_{\rm 200c}$. We demonstrate that baryonic feedbackmechanisms significantly redistribute gas, lowering the baryon fractions insidehaloes while simultaneously accumulating this material outside the virialradius. To understand this large-scale baryonic redistribution and identify thedominant physical processes responsible, we examine several variants of TNGthat selectively exclude stellar and AGN feedback, cooling, and radiation. Wefind that heating from the UV background in low-mass haloes, stellar feedbackin intermediate-mass haloes, and AGN feedback in groups ($10^{12} \leq M_{\rm200c}/{\rm M_{\odot}}<10^{14}$) are the dominant processes. Galaxy clusters arethe least influenced by these processes on large scales. We introduce a newhalo mass-dependent characteristic scale, the closure radius $R_{\rm c}$,within which all baryons associated with haloes are found. For groups andclusters, we introduce a universal relation between this scale and the halobaryon fraction: $R_{\rm c}/R_{\rm 200c,500c}-1=\beta(z)(1-f_{\rm b}(<R_{\rm200c,500c})/f_{\rm b,cosmic})$, where $\beta(z)=\alpha\,(1+z)^\gamma$, and$\alpha$ and $\gamma$ are free parameters fit using the simulations.Accordingly, we predict that all baryons associated with observed X-ray haloescan be found within $R_{\rm c}\sim 1.5-2.5 R_{\rm 200c}$. Our results can beused to constrain theoretical models, particularly the physics of supernova andAGN feedback, as well as their interplay with environmental processes, throughcomparison with current and future X-ray and SZ observations.

Feedback reshapes the baryon distribution within haloes, in halo outskirts, and beyond: the closure radius from dwarfs to massive clusters