  In his work extending rational simple connectedness to schemes with higher
Picard rank, Yi Zhu introduced hypotheses for schemes insuring that the
relative Picard functor is representable and is \'{e}tale locally constant with
finite free stalks. We give examples showing that one cannot eliminate any of
the hypotheses and still have a representable Picard functor that is locally
constant with finite free stalks. We also prove that the hypotheses are
compatible with composition and with hyperplane sections.
