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They'll usually just leave the port. There is a very, very small chance that you'll capture a few ships or occasionally the whole fleet, and this chance is increased if you have ships outside the harbor. If the port faces onto a canal/strait like the Suez Canal or Straits of Gibraltar, then since they can't go into the seazone they'll stay in port - your port - but they still won't change sides. They'll disappear when you annex.