It depends on the individual circumstances involved. There are bans for different reasons. A simple overstay exceeding 180 days invokes a 3 year ban. Overstay of one year invokes a 10 year ban. Certain removals invoke a 5, 10, 20 year or lifetime ban. Some bans can be ended early via a waiver but it depends on the individual circumstances as to availability of a waiver. Also, some waivers allow for a non-immigrant entry and others are for immigrant entry. Written notice is given in a formal removal and written notice is given when refused entry. Sometimes notice is given when applying for a visa abroad.