A morphism of schemes which is formally unramified, universally closed, and a monomorphism is a closed immersion. Is it possible to characterize morphisms which are formally etale and universally closed?

If $f$ is a morphism between locally noetherian schemes $X$ and $Y$ which is formally etale and universally closed, then it will be quasi-compact, whence etale and moreover quasi-finite. In this case, I am tempted to conjecture that, if $f$ is surjective, then

$$X \cong \bigsqcup_{i=1}^{n} Y$$ in this case. This is probably overly optimistic, but I have something like this in mind when I use the word "characterize."