hi,

how does the effect exaclty work? regarding "palyers assign their own indirect damage."?

where on the opponent's capital goes this damage? can it be divided between example quest zone and kingdom?

its the same as any other indirect damage. The opponent will assign the damage however he/she chooses among his units and/or capital. They cannot assign more damage than what is needed to kill something and they cannot assign damage to a burning zone of their capital.