Gradients of cellular activities are ubiquitous in embryonic development. It is widely believed that the inhomogeneous spatial distribution of a morphogen would be able to set up such gradients. But how then does the morphogen propagate in the first place? Straightforward molecular diffusion is often proposed as a possible mechanism. We first show that, surprisingly, the mere binding of the diffusing morphogen to its membrane receptors suffices to prevent the establishment of a concentration-based positional signalling system. Instead, a flat, saturated distribution of receptor-bound morphogen builds up. Because the distribution spreads gradually from the morphogen source, however, cells may still know their position if they are able to integrate the morphogen signal in time. The irregularities of diffusion in the complex extracellular medium would in fact be partially compensated for by such time summation. Another, non-exclusive possibility is that morphogen transport does not occur by simple diffusion only. We put forth a novel model of receptor-aided, directed diffusion that achieves a spatial distribution of morphogen. Our model is based, as an illustration, on the properties of members of the TGFbeta family of molecules. We show that two simple hypotheses regarding the kinetics of TGBbeta binding to its receptors suffice to establish a remarkable transfer mechanism whereby a morphogen such as activin could be both propagated along cell membranes, and transferred between cells that are in contact. The model predicts that morphogen propagation properties depend strongly on the closeness of cell-cell appositions, does not necessitate protein synthesis, accumulation or slow degradation (in contrast to the diffusion/time integration model), and that the morphogen is localised mostly on or close to cell membranes.