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We consider the BEC-Skyrme model which is based on a Skyrme-type model with apotential motivated by Bose-Einstein condensates (BECs) and, in particular, westudy the Skyrmions in proximity of a domain wall that inhabits the theory. Thetheory turns out to have a rich flora of Skyrmion solutions that manifestthemselves as twisted vortex rings or vortons in the bulk and vortex handlesattached to the domain wall. The latter are linked open vortex strings. Wefurther study the interaction between the domain wall and the Skyrmion andbetween the vortex handles themselves as well as between the vortex handle andthe vortex ring in the bulk. We find that the domain wall provides a largebinding energy for the solitons and it is energetically preferred to stay asclose to the domain wall as possible; other configurations sticking into thebulk are metastable. We find that the most stable 2-Skyrmion is a torus-shapedbraided string junction ending on the domain wall, which is produced by acollision of two vortex handles on the wall, but there is also a metastableconfiguration which is a doubly twisted vortex handle produced by a collisionof a vortex handle on the wall and a vortex ring from the bulk.

Baryonic handles: Skyrmions as open vortex strings on a domain wall