In this talk we look at a three-dimensional version of a twodimensional polymer in a poor resolvent that was analysed in detail by P. Carmona, G.B. Nguyen and N. Petrelis. Polymers are partially directed self-avoiding walks. Each pair of non-consecutive nearestneighbour monomers contributes a negative energy to the interaction Hamiltonian. The interaction strengths are  0 for monomers in di erent hyperplanes and  0 for monomers in the same hyperplane. We derive a variational formula for the excess free energy per monomer ~ f( ; ), and prove that there is a collapse transition between an extended phase E = f ;  0: ~ f( ; ) > 0g and a collapsed phase C = f ;  0: ~ f( ; ) = 0g. We identify the shape of the critical
curve separating the two phases, and obtain information on the typical behaviour of the polymer in the two phases. Work in progress with N. Petrelis (Nantes).