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We show the existence of an infinite collection of hyperbolic knots whereeach of which has in its exterior meridional essential planar surfaces ofarbitrarily large number of boundary components, or, equivalently, that each ofthese knots has essential tangle decompositions of arbitrarily large number ofstrings. Moreover, each of these knots has in its exterior meridional essentialsurfaces of any positive genus and (even) number of boundary components. Thatis, the compact surfaces that have a meridional essential embedding into ahyperbolic knot exterior have meridional essential embeddings into each ofthese hyperbolic knots exteriors.

Infinitely many meridional essential surfaces of bounded genus in hyperbolic knot exteriors