“…(d) We say that C is tangent-filling if every point P ∈ P 2 (F q ) lies on a tangent line T Q C to the curve C at some smooth F q -point Q. Regarding the literature, we note that curves satisfying (a) have been thoroughly studied in many papers ranging from foundational work [CHKT00, GK09,GGS10] to the more recent discoveries [BM18,BLM23]. The curves satisfying (b) have been analyzed by [HK13,DC18,Hom20].…”