Does taking an open battlefield or moving units to a battlefield you already control start a showdown?

Ruling: Taking an open battlefield starts a showdown. Moving units to a battlefield you already control does not start a showdown unless the move triggers an ability.

Sequence:

• When units move, a cleanup occurs
• During cleanup, any triggered abilities are processed
• At the very end of cleanup, a showdown starts if one should start
• Control of a battlefield being contested (even from no one) triggers a showdown

Nuances:

• Moving to an empty battlefield counts as contesting control, so it starts a showdown
• Moving to your own battlefield only opens a response window if the move causes an ability to trigger and create a chain
• A cleanup after conquering only occurs if an ability was triggered due to conquering, once the chain it created is emptied