Removes the phosphate from trehalose 6-phosphate to produce free trehalose. Is specific for trehalose 6-phosphate. Does not possess activity toward glucose, sucrose or fructose 6-phosphates. Regulates inflorescence branching. Required to establish the correct identity and determinacy of axillary meristems in both male and female inflorescences. May act through a sugar signal that moves into axillary meristems. Acts upstream of RA1. May have a transcriptional regulatory function. alpha,alpha-trehalose 6-phosphate + H2O = alpha,alpha-trehalose + phosphate Glycan biosynthesis; trehalose biosynthesis. Expressed in axillary inflorescence meristems. Additional long branches in tassels and abnormal long branches at their bases in ears. Abnormal identity of axillary meristems. Belongs to the trehalose phosphatase family.