The Oath of Vengeance paladin's Powerful Justice replaces the paladin's normal Aura of Justice:
Powerful Justice (Su)
At 11th level, an oathbound paladin may spends one use of her smite evil ability to grant her allies within 10 feet the ability to smite evil, except they only gain the paladin’s bonus to damage, not her smite’s attack bonus or ability to bypass DR.
This ability replaces aura of justice.
Once Powerful Justice is used, how long can the paladin's party members "hold onto" the ability to smite evil? Must it be used in the round immediately after Powerful Justice is activated, or can the allies wait until hours later before activating their smite?
Once the ally uses smite evil, it lasts as long as a normal smite evil would, rather than capping at a minute like Aura of Justice (see e.g. Paladin of Vengeance: Powerful Justice?). I'm not asking how long the smite lasts once it's activated, I'm asking how long a party member can wait before activating their smite.