Large-scale pattern formation is a frequently occurring phenomenon in biological organisms, and several local interaction rules for generating such patterns have been suggested. A mechanism driven by feedback between the plant hormone auxin and its polarly localized transport mediator PINFORMED1 has been proposed as a model for phyllotactic patterns in plants. It has been shown to agree with current biological experiments at a molecular level as well as with respect to the resulting patterns. We present a thorough investigation of variants of models based on auxin-regulated polarized transport and use analytical and numerical tools to derive requirements for these models to drive spontaneous pattern formation. We find that auxin concentrations in neighboring cells can feed back either on exocytosis or endocytosis and still produce patterns. In agreement with mutant experiments, the active cellular efflux is shown to be more important for pattern capabilities as compared to active influx. We also find that the feedback must originate from neighboring cells rather than from neighboring walls and that intracellular competition for the transport mediator is required for patterning. The importance of model parameters is investigated, especially regarding robustness to perturbations of experimentally estimated parameter values. Finally, the regulated transport mechanism is shown to be able to generate Turing patterns of various types.