Does Yone's conquer ability trigger when using Void Assault to move him to a battlefield that becomes uncontrolled?

Ruling: Yes, Yone's conquer ability triggers in both scenarios where Void Assault results in him conquering a battlefield that was uncontrolled.

Sequence:

Version 1 (Clearing an enemy-controlled battlefield):

• Void Assault moves Yone to an enemy-controlled battlefield (applying Contested status) and moves the last enemy unit out
• During cleanup, before the showdown opens, the opponent loses control per Rule 187.4.c because no combat/showdown is ongoing yet
• The battlefield becomes uncontrolled
• The non-combat showdown resolves and Yone establishes control, triggering his ability

Version 2 (Moving into an uncontrolled battlefield with a surprise defender):

• Void Assault moves Yone into an uncontrolled battlefield (applying Contested status), then pulls an enemy unit there
• A combat opens with Yone as attacker and the enemy as surprise defender
• The battlefield remains uncontrolled throughout the combat
• If Yone wins and establishes control, his ability triggers

Nuances:

• Simply moving units into a battlefield does not establish control
• The surprise defender does not make the battlefield controlled by their owner