By representation, per stirpes and the per capita systems, for Arizona trustees

The three systems, in one sentence each

Strict per stirpes — the division always begins at the children’s generation, one share per child living or deceased with descendants living; a deceased child’s share splits among that child’s own descendants. Arizona’s statutes give an instrument’s "per stirpes" no definition — a trust that uses the words is read on its own terms.

Per capita with representation — divide at the nearest generation with a surviving member: one share for each survivor there and for each deceased member who left descendants; a deceased member’s share passes down to that member’s own descendants. Not Arizona’s statutory default; a trust that wants it says so in its own words.

Per capita at each generation — divide at the nearest generation with survivors; the deceased members’ shares are combined and divided equally among the next generation’s takers, so equally-near relatives take equally. In Arizona this is the statutory meaning of "by representation" (A.R.S. § 14-2106(A)), the default for an intestate estate passing to descendants (§ 14-2103(1)).

The same family tree can come out differently under different governing words — which is why the instrument controls. Arizona’s statute defines "by representation" for an intestate estate (A.R.S. § 14-2106) and gives an instrument’s "per stirpes" no definition; a trust may define its own scheme or name alternate takers, and reading a particular instrument against the statute is licensed-attorney work. A surviving spouse’s intestate share depends on whether the surviving issue are also the spouse’s issue, and the decedent’s one-half of the community property passes with the separate property (§ 14-2102) — the other half of the community property is the surviving spouse’s own, never part of the estate.