This paper presents experimental research on wall slip and extrusion instability behavior of a series of monodisperse 4-arm star polybutadienes (PBD) of different molecular weights during fast capillary flow. The star PBDs reveal a slope of 3.0 in the capillary flow curve, showing a faster non-linear response than linear PBDs. The global stick-slip transition of star PBD is weaker than linear PBD of the same molecular weight, as indicated by a smaller extrapolation length b of star PBD. The "sharkskin" fracture takes place without a global stick-slip transition for a star PBD with molecular weight of 200 K, suggesting the sharkskin instability may not originate from an oscillating stick-slip transition at die exit. The flow splitting, i.e., the phenomenon that the extrudate breaks into two or more branches after the die exit, is observed in star PBDs with molecular weights higher than 200 K. The flow splitting, accompanied by a precession motion, is found to be an exit instability behavior. The flow splitting is related to the long bulk relaxation time of the star polymers and more likely to occur in a solid-like state, where the storage modulus G' is higher than the loss modulus G'. A "rotating-breaking" hypothesis is proposed to explain the flow splitting and sharkskin instability behavior of star PBDs based on a stretch induced rupture at die exit in a rotating pattern.