My aunt passed with no will. She had no kids and husband is decede. Her brother (my dad) is the only sibling alive. He has 4 kids. My Aunt & Dad's half sister (who is deceded) has 3 kids. How will her assets be divided? She has about $100,000 in cash, should he go through the courts to be appointed administrator of her estate?

First, your Dad should indeed be appointed administrator by the probate court. As her only remaining sibling, he is her closest living relative and so this should be straight-forward.

As for who gets what - there is one living sibling (your dad) and one deceased (the half-sister). I believe her estate will be divided in half - one half to your dad and one half to the half-sister's children per stirpes (i.e. each of her three children get 1/6). Here's is a chart that explains it: Intestacy Chart (http://www.lyster.com/estates/post_mortem_probate/intestacy_chart.htm) Note that the since your aunt had no spouse nor children, the order or precedence is:

1. To decedent's parents equally; - since they are not surviving, we skip this.
2. To the issue of parents or either of them, equally if all of the same degree of kinship; I highlighted the part that makes the half-sister an equal inheritor to your father. Since she is dead, her share is split among her three children.