"Head of Household" Designation for adult children living with Parents.

When does an adult child become "Head of Household". I'm new to the calling and trying to clean up the records. Our ward has several adult children who are in their mid - 20's or older but are listed under their father, but also several that seem to be in the same circumstances but are considered "head of household". Is there a rule I can follow?

You may want to review the Help Center article Make Changes to Member Households. As it says, ultimately it's the bishop's decision. But in particular, if the bishop and Elder's quorum and/or Relief Society feel they should have different ministering brethren then they need to be a separate household. But in if they have the same ministering assignments as the family then it could go either way.

There is fairly lengthy thread on this subject here: https://tech.lds.org/forum/viewtopic.php?t=5513

It's fairly old but does include various things that can be considered by the bishop in making the decision.