In this talk I will present some answers to the question when every specialisation from a \kappa-saturated extension of
a Zariski structure is \kappa-universal? I will show that for algebraically closed fields, all specialisations from a \kappa-
saturated extension is \kappa-universal. More importantly, I will consider this question for finite and infinite covers of
Zariski structures. In these cases I will present a counterexample to show that there are covers of Zariski structures
which have specialisations from a \kappa-saturated extension that are not \kappa-universal. I will present some natural
conditions on the fibres under which all specialisations from a \kappa-saturated extension of a cover is \kappa-universal.
I will explain how this work points towards a prospective Ladder Theorem for Specialisations and explain difficulties and
further works that needs to be considered.
