Reference request: an algebraic stack whose closed points have no automorphisms is an algebraic space The question is stated in the title. I think BCnrd states in a comment here
Is every (Artin/DM) algebraic stack fibered in sets an algebraic space?
that while the answer is not found in Laumon & Moret-Bailly, but that it is nevertheless true. Does anyone know of a reference? (Also: I only care about stacks over $\mathbb{C}$, if that makes a difference.)
 A: Here's a counterexample to your title question, that is not a counterexample to BCnrd's claim:
Let $Y =\operatorname{Spec} \mathbb{C}[[t]]$.  This scheme has a closed point and an open generic point.  Let $Z$ be the scheme formed by gluing two copies of $Y$ by the identity map on generic points.  This is a non-separated scheme with an action of a group of order two that fixes the generic point and switches the two closed points.  Let $X$ be the stack quotient of $Z$ by this action.
$X$ is not an algebraic space, since the image of the generic point of $Z$ has a nontrivial stabilizer.  In particular any geometric point (meaning a map from the spectrum of an algebraically closed field) that factors through the generic point of $Z$ will have nontrivial stabilizer.  The topological space $|X|$ (defined in Champs Algebriques 5.5) only has one closed point, and the automophism group of any element in its equivalence class is trivial.
A: In case you're still looking for a reference I Lemma 2.3.9 of Abramovich and Hassett stable varieties with a twist should do it (consider the map to a point, which has no automorphisms, which by assumptions is injective on automorphism groups)
http://arxiv.org/pdf/0904.2797v1.pdf
