Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$1 \ll D \ll N^\nu$</EquationSource> </InlineEquation> (<InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\nu=3/4$</EquationSource> </InlineEquation> is the Flory exponent). For the simulations we...</equationsource></inlineequation></equationsource></inlineequation>