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I can imagine that two things might be denoted by the term immigration area:
A place where immigration controls take place. This is more commonly known as passport control, or perhaps immigration control, or an immigration checkpoint.
A place where people are considered, for immigration purposes, to be in "international territory." This is more precisely known as the international area of the airport, or the transit area. (It is also sometimes called airside, or the sterile area, but this is ambiguous, because it might refer to areas protected by security screening that are domestic territory for immigration purposes.)
Airports handle the second item differently. For example, in most Schengen area airports, you can transfer to another flight within the international transit area without passing through immigration control, provided that you are arriving from a point outside the Schengen area and transferring to a flight to somewhere outside Schengen area.
On the contrary, in the United States, all arriving international passengers must pass through the immigration checkpoint before they can reach any connecting flights. In cases like this, the international area of the airport contains only arriving passengers, and comprises the corridors connecting the arrival gates to the immigration checkpoint.