We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semidilute solutions. Our main result is that the free energy for overlapping n chains is independent of chain length and scales as n 9=4 , slowly crossing over to n 3 , as n increases. For strongly confined polymers inside a spherical cavity, we show that rearranging the chains does not cost an

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... free energy. Our results imply that, during cell cycle, global reorganization of eukaryotic chromosomes in a large cell nucleus could be readily achieved.