We construct an infinite collection of knots with the property that any knot in this family has –string essential tangle decompositions for arbitrarily high .
"The number of strings on essential tangle decompositions of a knot can be unbounded." Algebr. Geom. Topol. 16 (5) 2535 - 2548, 2016. https://doi.org/10.2140/agt.2016.16.2535