Wills, Trusts, and Estates
Under the English Per Stirpes system, shares are divided equally to children, then if dead, divided again to their children. Thus, grandchildren with fewer siblings get more money.
English Per Stirpes has vertical equality—bloodlines get equal amounts.
Under the Modern Per Stirpes system, shares are divided equally to children, but if all children are dead, the property is divided among grandchildren. Thus, all grandchildren get the same amount if all the children are dead. If some children survive, it is the same as English Per Stirpes.
Modern Per Stirpes applies the same with grandchildren and great-grandchildren. The division does not occur until the first generation with a live taker.
Modern Per Stirpes has horizontal equality—children/grandchildren get equal amounts—whenever all children are dead.
Under the Per Capita at Each Generation system, shares are divided equally to the first living descendant generation (where it is divided equally among the living children and children with living descendants), then if one or more are dead, the reminder is divided again to their children. Thus, all "grandchildren" always get the same amount.
Per Capita at Each Generation has horizontal equality—children/grandchildren get equal amounts—always.
The UPC uses Per Capita at Each Generation. UPC § 2-103(a).
Descendants' surviving spouses (i.e., children-in-law) never get anything in most jurisdictions.