  We study the tractability of conjunctive query answering for queries with
unbounded arity. It is well known that tractability of the problem can be
characterised in terms of the queries treewidth under the assumption of bounded
arity. We extend this result to cases with unbounded arity but degree 2. To do
so, we introduce hypergraph dilutions as an alternative method to primal graph
minors for studying substructures of hypergraphs. Using dilutions we observe an
analogue to the Excluded Grid Theorem for degree 2 hypergraphs. In consequence,
we show that that the tractability of conjunctive query answering can be
characterised in terms of generalised hypertree width. A similar
characterisation is also shown for the corresponding counting problem. We also
generalise our main structural result to arbitrary bounded degree and discuss
possible paths towards a characterisation of the bounded degree case.
