  We study the partial entanglement entropy (PEE) aspects of the holographic
BCFT setup with an entanglement island, inspired by the holographic triality of
the AdS/BCFT setup developed in the recent study on the black hole information
problem, and the "PEE=CFF (component flow flux)" prescription, which is
proposed recently to investigate the holographic PEE in the framework of bit
thread formulation. Our study provides a bit thread description of the AdS/BCFT
setup, which characterizes the specific entanglement details between the
different parts of the system with an entanglement island, and may provide
further insight into the black hole information problem. Furthermore, we show
that in the context of island, one should distinguish between the fine-grained
PEE and the semi-classical PEE. Interestingly, similar to the island rule of
the fine-grained entropy in the semi-classical picture, we also propose the
island rules of the fine-grained PEE.
