Abstract We are using trichome (hair) morphogenesis as a model to study how plant cell shape is controlled. During a screen for new mutations that affect trichome branch initiation in Arabidopsis, we identified seven new mutants that show a reduction in trichome branch number from three branches to two. These mutations were named furca, after the Latin word for two-pronged fork. These seven recessive mutations were placed into four complementation groups that define four new genes: FURCA1, FURCA2, FURCA3 and FURCA4. The trichome branch number phenotype indicates that the FURCA genes encode positive regulators of trichome branch initiation. Analysis of double mutants suggests that primary and secondary branch initiation events are not genetically distinct, but rely on the levels of partially redundant groups of regulators of trichome branch initiation. Based on the analysis of both epistatic and additive genetic interactions between the FURCA genes and other genes that control trichome branch number, we propose a model that explains how these genes interact to control trichome branch initiation. This model successfully predicts the phenotypes of all the single and double mutants examined and suggests points of control of the trichome branch pathway.