We assume a scenario in which transition discs (i.e. discs around young stars that have signatures of cool dust but lack significant near infra-red emission from warm dust) are associated with the presence of planets (or brown dwarfs). These are assumed to filter the dust content of any gas flow within the planetary orbit and produce an inner `opacity hole. In order to match the properties of transition discs with the largest (~50 A.U. scale) holes, we place such `planets at large radii in massive discs and then follow the evolution of the tidally coupled disc-planet system, comparing the systems evolution in the plane of mm flux against hole radius with the properties of observed transition discs. We find that, on account of the high disc masses in these systems, all but the most massive `planets (100 Jupiter masses) are conveyed to small radii by Type II migration without significant fading at millimetre wavelengths. Such behaviour would contradict the observed lack of mm bright transition discs with small (<10 A.U.) holes. On the other hand, imaging surveys clearly rule out the presence of such massive companions in transition discs. We conclude that this is a serious problem for models that seek to explain transition discs in terms of planetary companions unless some mechanism can be found to halt inward migration and/or suppress mm flux production. We suggest that the dynamical effects of substantial accretion on to the planet/through the gap may offer the best prospect for halting such migration but that further long term simulations are required to clarify this issue.
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