As a champ mentioned below, since you lived together, you do not need to file form 8332.
Since you were legally divorced, whoever provided the majority of the support would be the one that could claim Head of Household. A requirement to claiming Head of Household is that you must have paid more than half of the cost of keeping up a home.
@JOHNNY3 (Edited 01/21/2022 @ 6:42AM PST)
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