We present: i) an example of a Banach space of universal disposition that is not separably injective; ii) an example of a Banach space of universal disposition with respect to finite dimensional polyhedral spaces with the Separable Complementation Property; iii) a new type of space of universal disposition nonisomorphic to the previous existing ones.

The research of the first author was partially supported by project MTM2013-45643-C02-1-P