Branching of single cells is controlled by intracellular or extracellular cues that lead to the establishment of a polarity axis and subsequently to the local activation of growth activity. Three model cell types in Arabidopsis, that elucidate different mechanisms of branch formation in single cells, are considered in this review. Trichomes serve as a model to study how multiple branches are formed in a predictable manner. Epidermal pavement cells enable study of pathways that integrate extracellular signals and facilitate coordinated growth within a tissue. The analysis of root hairs reveals information about how branch formation can be inhibited. The mechanisms involved in branch formation at the level of single plant cells seem to be entirely different from those leading to branching at the level of tissues or the whole organism. Whereas the latter ultimately control the temporal and spatial coordination of cell divisions, at least in plants, branching at the single cell level regulates localized cell growth or expansion. This is achieved in several steps. Initially, the integration of external and internal cues creates the positional information for the proper initiation of branches. This information is best understood in three epidermal cell types in Arabidopsis (Fig. 1): leaf trichomes, leaf pavement cells and root hairs. Leaf trichomes exemplify a cell type in which the spatial orientation of the branches is strictly correlated with respect to the leaf axis indicating the existence of a three-dimensional prepattern. Leaf pavement cells are initially round or square and then initiate branches to adopt the shape of a piece of a jigsaw puzzle. Where these branches form is not predictable but their formation is always coordinated with morphogenesis in neighbouring cells. Arabidopsis root hairs, which are also composed of single cells, are normally not branched but certain mutants and drug treatments lead to their branching. Root hairs therefore serve as a model to study how branching is suppressed. In this chapter we will summarize the current view of how branch formation is controlled in these three cell types. [ABSTRACT FROM AUTHOR]