<p>Spatial distributions of morphogens provide positional information in developing systems, but how the distributions are established and maintained remains an open problem. Transport by diffusion has been the traditional mechanism, but recent experimental work has shown that cells can also communicate by filopodia-like structures called cytonemes that make direct cell-to-cell contacts. Here we investigate the roles each may play individually in a complex tissue and how they can jointly establish a reliable spatial distribution of a morphogen. To this end, we formulate models that capture fundamental aspects of various cytoneme-based transport mechanisms. In simple cases, exact solutions are attainable, and in more complex cases, we discuss results of numerical simulations.</p>