  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 semi-dilute solutions. Our main result
is that the free energy for overlapping $n$ chains is \emph{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 additional free energy. Our
results imply that, during cell cycle, \emph{global} reorganization of
eukaryotic chromosomes in a large cell nucleus could be readily achieved.
