If my opponent has Stellacorn Herder at a battlefield and a Zhonya's Hourglass at their base, and I play Smite targeting Stellacorn, what happens? Is Stellacorn banished? Or is it recalled and saved from Zhonya's?

Stellacorn Herder will be saved and recalled to your opponent's base; it will not be banished.

The Breakdown

This interaction involves a conflict between two replacement effects: the "banish" effect from Smite and the protective effect from Zhonya's Hourglass.

1. The Trigger: When Smite deals 3 damage to the Stellacorn Herder (which has 3 Might), the unit is marked to "die."
2. Replacement Effects: Because both Smite (which would replace the "death" event with a "banish" event) and Zhonya's Hourglass (which would replace the "death" event with "heal, exhaust, and recall") apply to the same "die" event, Rule 372 and the related FAQ #10635 apply.
3. Choosing the Order: The controller of the unit—your opponent—gets to decide the order in which these replacement effects are applied.
4. The Saving Sequence:
   • Your opponent chooses to apply the Zhonya's Hourglass replacement effect first.
   • Zhonya's Hourglass replaces the death event entirely: it heals the unit, exhausts it, and recalls it to the base. It also sends itself (the Zhonya's Hourglass) to the trash.
   • Since the "die" event has now been fully replaced and no longer occurs, Smite's replacement effect no longer has a valid "death" event to modify. It fails to apply, and the unit is not banished.

Summary: Your opponent chooses to use the protective gear first. The Stellacorn Herder survives, is recalled to their base (exhausted), and the Zhonya's Hourglass is trashed. The banishment never happens.