My grandmother has a large estate which she left to her two children. The Will states the following "I direct that all my residuary estate be divided into as many equal shares as there are children of mine then living and then deceased by living descendants then living and I leave one share to each living child of mine and one share to living descendants collectively of each deceased such issue by take of right of representation." I have never had a relationship with my father (her son) who was alive upon her death and I assume he does not plan on passing the estate on to me. Does this mean I do not have any rights to the estate as a descendant?

Correct. If your father had died before your grandmother, then you would be entitled to a share of his share. But since he was living then it goes to him. Whether he leaves his share to you is now up to him.

Your father is under no requirement to share with you - estranged or not estranged.

Scott is - as usual - 100% on.

Right. This formula provides for distribution per stirpes (http://en.wikipedia.org/wiki/Per_stirpes), although it is very inartfully worded.

You would be a descendent of "C" in the diagram below (on left).

http://upload.wikimedia.org/wikipedia/en/thumb/0/05/Comparison_of_per_stirpes_and_per_capita_inheritan ce.PNG/500px-Comparison_of_per_stirpes_and_per_capita_inheritan ce.PNG