What does the Dissolve Empire casus belli cost?

piety; the amount depends on the titles, claims and distance, worked out when you declare.

Casus belli · Holy wars

Dissolve Empire

The war is called “Dissolve Empire of the defender”

Dissolve Empire is a casus belli in Crusader Kings III (holy wars). If the attacker wins: The Excommunicated Emperor is stripped of their Empire Title, which is destroyed. If the defender wins: The attempt to dissolve the Empire has failed. Declaring it costs piety. Patch 1.20.0.3, from game/common/casus_belli_types/00_dissolve_empire_cb.txt.

Quick answers (3)

What do you get for winning a Dissolve Empire war in CK3?: The Excommunicated Emperor is stripped of their Empire Title, which is destroyed (patch 1.20.0.3).
What happens on a white peace?: The war ends inconclusively. Neither side gains an advantage.
What does the Dissolve Empire casus belli cost?: piety; the amount depends on the titles, claims and distance, worked out when you declare.

How the war ends

Attacker wins

The Excommunicated Emperor is stripped of their Empire Title, which is destroyed.

White peace

The war ends inconclusively. Neither side gains an advantage.

Defender wins

The attempt to dissolve the Empire has failed.

If the war becomes invalid

The … has ended: it was no longer valid to continue.

Who can declare it

The game shows no text of its own for these conditions; the script is below.

Every holy wars war (the group's allowed_for_character) (24 lines of game script)

OR = {
	top_liege = this
	any_liege_or_above = {
		faith = prev.faith
		count = all
	}
}
faith = {
	NOR = {
		has_doctrine_parameter = unreformed
		AND = {
			has_doctrine_parameter = holy_wars_forbidden
			NOT = {
				prev = {
					has_character_flag = bonus_major_holy_war
				}
			}
		}
	}
}
herders_and_tributary_constraints = yes
pam_personal_pacifism_offensive_war_ban_trigger = yes
tgp_dynastic_cycle_offensive_wars_ban_trigger = yes
tgp_war_ban_all_ministers_trigger = yes

As written in game/common/casus_belli_groups/00_casus_belli_groups.txt.

Attacker (allowed_for_character) (7 lines of game script)

rite = {
	rite_has_parameter = excommunication_active
}
empire_faith_gate_enabled_trigger = yes
NOT = {
	has_trait = excommunicated
}

As written in game/common/casus_belli_types/00_dissolve_empire_cb.txt.

Defender (allowed_against_character) (37 lines of game script)

scope:defender = {
	top_liege = this
	any_held_title = {
		tier >= tier_empire
	}
	has_trait = excommunicated
	faith = scope:attacker.faith
	rite = {
		rite_has_parameter = excommunication_active
	}
	trigger_if = {
		limit = {
			scope:attacker = {
				is_ai = yes
			}
		}
		efg_contested_empire_grace_period_elapsed_trigger = yes
	}
	trigger_else = {
		always = yes
	}
}
scope:attacker = {
	NOR = {
		liege = scope:defender
		has_trait = excommunicated
	}
	trigger_if = {
		limit = {
			is_ai = no
			highest_held_title_tier < tier_empire
		}
		any_neighboring_top_liege_realm_owner = {
			this = scope:defender
		}
	}
}

As written in game/common/casus_belli_types/00_dissolve_empire_cb.txt.

When it can start (valid_to_start) (1 line of game script)

always = yes

As written in game/common/casus_belli_types/00_dissolve_empire_cb.txt.

Cost to declare

Costs piety. The amount is worked out when you declare (by the titles targeted, claims, distance and more), so the script is shown as written:

Cost (7 lines of game script)

piety = {
	add = {
		value = 200
		desc = CB_BASE_COST
	}
	multiply = common_cb_piety_cost_multiplier
}

As written in game/common/casus_belli_types/00_dissolve_empire_cb.txt.

Source: game/common/casus_belli_types/00_dissolve_empire_cb.txt and the English localisation, Crusader Kings III 1.20.0.3. “The attacker”, “the defender” stand where the game names the character; “…” marks other words it fills in during play.