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Under per stirpes, each branch of a family receives an equal share. So, if you have three children who each have two children and a child of yours predeceases you, under per stirpes distribution child 1 would inherit 1/3, child 2 would inherit 1/3, and grandchild 1 would inherit 1/6 as would grandchild 2. Another phrase for this same concept, that is not in Latin, is "by right of representation".
When working with clients I routinely ask whom should receive an inheritance if the person they just named would predecease them. And it is here that per stirpes or by right of representation is most commonly used.
Remember, a blog is not an attorney. Please consult a lawyer in your area for advice on your specific situation.