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A graph parameter is self-dual in some class of graphs embeddable in some surface if its value does not change in the dual graph by more than a constant factor. We prove that the branchwidth of connected hypergraphs without bridges and loops that are embeddable in some surface of Euler genus at most g is an (1,g)-self-dual parameter. This is the first proof that branchwidth is an additively self-dual width parameter., Comment: 10 pages

A graph is called a pseudoforest if none of its connected components contains more than one cycle. A graph is an apex-pseudoforest if it can become a pseudoforest by removing one of its vertices. We identify 33 graphs that form the minor-obstruction set of the class of apex-pseudoforests, i.e., the set of all minor-minimal graphs that are not apex-pseudoforests.