What do you get for winning a Seize Hegemonic County war in CK3?

The attacker gains the contested Title (patch 1.20.0.3).

What does the Seize Hegemonic County casus belli cost?

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

Casus belli · Celestial

Seize Hegemonic County

Seize Hegemonic County is a casus belli in Crusader Kings III (celestial). If the attacker wins: The attacker gains the contested Title. If the defender wins: The defender keeps the contested Title. Declaring it costs prestige. The war goal is worth 80% war score. Patch 1.20.0.3, from game/common/casus_belli_types/10_tgp_china_wars.txt.

Quick answers (3)

What do you get for winning a Seize Hegemonic County war in CK3?: The attacker gains the contested Title (patch 1.20.0.3).
What happens on a white peace?: The defender keeps the contested Title.
What does the Seize Hegemonic County casus belli cost?: prestige; the amount depends on the titles, claims and distance, worked out when you declare.

How the war ends

Attacker wins

The attacker gains the contested Title.

White peace

The defender keeps the contested Title.

Defender wins

The defender keeps the contested Title.

If the war becomes invalid

The … has ended: the defender no longer … the County.

Who can declare it

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

Every celestial war (the group's allowed_for_character) (6 lines of game script)

herders_and_tributary_constraints = yes
pam_personal_pacifism_offensive_war_ban_trigger = yes
tgp_war_ban_civilian_ministers_trigger = yes
NOT = {
	government_has_flag = government_is_theocracy
}

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

Attacker (allowed_for_character) (7 lines of game script)

OR = {
	has_title = title:h_china
	has_title = title:e_minister_grand_marshal
}
situation:dynastic_cycle ?= {
	has_situation_top_phase_parameter = dynastic_cycle_hegemon_unlocks_external_casus_belli
}

As written in game/common/casus_belli_types/10_tgp_china_wars.txt.

Defender (allowed_against_character) (6 lines of game script)

scope:defender = {
	NOR = {
		government_has_flag = government_is_landless_adventurer
		government_has_flag = government_is_herder
	}
}

As written in game/common/casus_belli_types/10_tgp_china_wars.txt.

When it can start (valid_to_start) (3 lines of game script)

scope:target ?= {
	is_neighbor_to_realm = scope:attacker.top_liege
}

As written in game/common/casus_belli_types/10_tgp_china_wars.txt.

Cost to declare

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

Cost (13 lines of game script)

prestige = {
	add = {
		value = 50
		desc = CB_BASE_COST
	}
	add = {
		value = 2.5
		multiply = scope:attacker.realm_size
		desc = CB_REALM_SIZE_COST
		max = 150
	}
	multiply = common_cb_prestige_cost_multiplier
}

As written in game/common/casus_belli_types/10_tgp_china_wars.txt.

Source: game/common/casus_belli_types/10_tgp_china_wars.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.