Is Zakat obligatory on all wealth that has reached the Nisab and on which a Hawl (full lunar year) has passed, or only on the remaining portion, in the event that part of the wealth is in dispute and a judicial ruling has been issued in favor of the adversary but has not yet been enforced?

Zakat must be paid on money that is undisputed if it reaches the nisab (threshold) and a full year has passed over it. As for disputed money: if you are certain it is your money, you must pay zakat on it along with what was previously due. If you are certain it is not your money, then there is no zakat due on you for it; rather, you must repent and return it to its owner. If the matter is unclear to you, then whoever is ruled to be its owner must pay its zakat. Jurists have stipulated the obligation of zakat on usurped and lost money once it returns to its owner. So, if usurped money is recovered or seized after one gains control over it, or if there is clear evidence for disputed money or if the judge becomes aware of it, zakat must be paid on the money for all past years.