We investigate the thermodynamic properties of a dilute solution of li
ving polymers confined between two solid repulsive walls. We consider
both the case of rigid and of flexible macromolecules. When the confin
ed system is taken to be at equilibrium with an external reservoir the
living polymers behave similarly to a polydisperse solution of unbrea
kable chains. However for closed gaps the behaviour is quite different
from a classical polymer solution because the worm-like micelles can
adapt their intrinsic polydispersity in order to release the confineme
nt constraint. In particular, for rigid living polymers this leads to
a divergence of the average chain-length in the limit of strong confin
ement, as well as to a non-monotonic behaviour of the pressure acting
on the walls.