When two people have been living together and they decide not to live together anymore, they are separated.
When married parents separate, their marriage is not over. They have to get a divorce to legally end a marriage.
Parents who separate often make a separation agreement that states who their children are going to live with and how they are going to divide their property. A separation agreement is not the same as a divorce, but it is a contract, which means that both parents sign it and then have to do what they have agreed to.
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