Pointwise surjective presentations of stacks

We show that any stack X of finite type over a Noetherian scheme has presentation X→X by such X(F)→X(F) is onto, for every or real closed field F. Under some additional conditions on X, we the same all perfect fields. prove similar results (some) Henselian rings. give two applications main result. One to counting isomorphism classes stacks rings Z/pn; other about relation between algebraic and Nash stacks.