Star-shaped molecules are of growing interest as organic optoelectronic materials. Here a detailed study of their photophysics using fluorescence depolarisation is reported. Fluorescence depolarisation dynamics are studied in branched oligofluorene-truxene molecules with a truxene core and well-defined three-fold symmetry, and are compared with linear fluorene oligomers. An initial anisotropy value of 0.4 is observed which shows a two-exponential decay with time constants of 500 fs and 3-8 ps in addition to a long-lived component. The femtosecond component is attributed to exciton localisation on one branch of the molecule and its amplitude reduces when the excitation is tuned to the low energy tail of the absorption spectrum. The picosecond component shows a weak dependence on the excitation wavelength and is similar to the calculated rate of the resonant energy transfer of the localised exciton between the branches. These assignments are supported by density-functional theory calculations which show a disorder-induced splitting of the two degenerate excited states. Exciton localisation is much slower than previously reported in other branched molecules which suggests that efficient light-harvesting systems can be designed using oligofluorenes and truxenes as building blocks. "