  Scattered factor (circular) universality was firstly introduced by Barker et
al. in 2020. A word $w$ is called $k$-universal for some natural number $k$, if
every word of length $k$ of $w$'s alphabet occurs as a scattered factor in $w$;
it is called circular $k$-universal if a conjugate of $w$ is $k$-universal.
Here, a word $u=u_1\cdots u_n$ is called a scattered factor of $w$ if $u$ is
obtained from $w$ by deleting parts of $w$, i.e. there exists (possibly empty)
words $v_1,\dots,v_{n+1}$ with $w=v_1u_1v_2\cdots v_nu_nv_{n+1}$. In this work,
we prove two problems, left open in the aforementioned paper, namely a
generalisation of one of their main theorems to arbitrary alphabets and a
slight modification of another theorem such that we characterise the circular
universality by the universality. On the way, we present deep insights into the
behaviour of the remainder of the so called arch factorisation by Hebrard when
repetitions of words are considered.
