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We continue study of some algebraic varieties (called resultantal varieties)started in a paper of A. Grishkov, D. Logachev "Resultantal varieties relatedto zeroes of L-functions of Carlitz modules". These varieties are related withthe Sylvester matrix for the resultant of two polynomials, from one side, andwith the L-functions of twisted Carlitz modules, from another side.Surprisingly, these varieties are described in terms of finite weighted rootedbinary trees. We give a (conjecturally) complete description of them, we findparametrizations of their irreducible components and their invariants: degrees,multiplicities, Jordan forms, Galois actions. Proof of the fact that thisdescription is really complete is a subject of future research. Maybe ageneralization of these results will give us a solution of the problem ofboundedness of the analytic rank of twists of Carlitz modules.

L-functions of Carlitz modules, resultantal varieties and rooted binary trees, II