The authors consider a lattice model for equilibrium polymerisation in a solvent proposed by Wheeler and Pfeuty. They include attractive interactions between first-neighbour monomers which belong to polymer chains but are not consecutive along a chain. In the limit of no dilution this model describes the collapse transition of a polymer in a poor solvent ( Theta -point). When no attractive interaction is present the model is appropriate for sulphur solutions, where a dilution tricritical point is observed. The thermodynamic properties of the model were studied by two kinds of calculations. The solution on the Bethe lattice shows a locus of tricritical points, including the Theta and dilution tricritical points. On a fractal lattice (3D Sierpinski gasket), the exact real space RG solution reveals that the Theta -point and the dilution tricritical point belong to the same universality class.