  This is the continuation of the article by the author that proves a broader
class of families admitting the theorem of restriction of sections other than
Abelian varieties and gives new examples of pseudo-N\'eron models. In this
work, we show that the techniques in the first paper give more general results
and more examples such that the theorem of restriction of sections holds. Also,
we give counter examples to show that the non-existence of rational curves is
not a necessary condition for such theorems. As an application, we prove a
result for Hodge classes of a certain weight which is similar to the result
about sections.
