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The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness (), the collapse transition is first order; it becomes second order only in the limiting case of zero bending stiffness (). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.