  We study ``disjoint" versions of the notions of trivial, locally trivial,
strictly singular and super-strictly singular quasi-linear maps in the context
of K\"othe function spaces. Among other results, we show: i) (locally) trivial
and (locally) disjointly trivial notions coincide on reflexive spaces; ii) On
non-atomic superreflexive K\"othe spaces, no centralizer is singular, although
most are disjointly singular. iii) No super singular quasi-linear maps exist
between superreflexive spaces although Kalton-Peck centralizers are super
disjointly singular; iv) Disjoint singularity does not imply super disjoint
singularity.
