In this paper, we study the fine structure of entanglement in holographic two-dimensional boundary conformal field theories (BCFT) in terms of the spatially resolved quasilocal extension of entanglement entropy - entanglement contour. We find that the boundary induces discontinuities in the contour revealing hidden localization-delocalization patterns of entanglement degrees of freedom. Moreover, we observe the formation of ``islands where the entanglement contour vanishes identically implying that these regions do not contribute to the entanglement at all. We argue that these phenomena are the manifestation of entanglement islands discussed recently in the literature. We apply the entanglement contour proposal to the recently proposed BCFT black hole models reproducing the Page curve - moving mirror model and the pair of BCFT in the thermofield double state. From the viewpoint of entanglement contour, the Page curve also carries the imprint of strong delocalization caused by dynamical entanglement islands.
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