firstname.lastname@example.org wrote: What is the largest rope size I can safely use for friction hitch on a half inch rope?
The best answer is "It depends". For a single ended split-tail a 1/2" rope of the same construction as your climbing line (assuming it's a 1/2" double-braid arborist line) works very well. If you want to use a "double-ended" split tail commonly called an "eye-to-eye" split tail, 10mm hitch cord works very well on half inch climbing line. I've never seen cordage sold by arborist gear suppliers for use as an eye-to-eye split tail larger than 10mm diameter.