The effects of surface segregation in a polydisperse system of "living polymers," confined between parallel solid surfaces, are studied by means of a lattice Monte Carlo (MC) simulation. For given density and temperature the system is characterized by exponential distribution of chain lengths established in the process of reversible equilibrium polymerization. The results of the calculations show that entropic effects cause a rearrangement of the species with different length into an "onion shell" structure. Thus for flexible chains preferential presence of shorter chains in the vicinity of the surface takes place, in contrast to the case of semi-rigid chains, when shorter chains deplete the region around the solid surface. In the case of adsorbing walls this surface segregation is enhanced. The study also reveals that isotherms of the adsorbed coverage and adsorbed amount are strongly influenced by the degree of chain stiffness.