Question

to which pair of taxpayers do the rules for children of divorced or separated parents apply

Answer 1

As per rules of IRS, You can’t claim a person as a dependent unless that person is your qualifying child or qualifying relative.

Tests To Be a Qualifying Child-

A child isn't a qualifying child unless he or she meets following conditions-

The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.
The child must be (a) under age 19 at the end of the year and younger than you (or your spouse if filing jointly), (b) under age 24 at the end of the year, a student, and younger than you (or your spouse if filing jointly), or (c) any age if permanently and totally disabled.
The child must have lived with you for more than half of the year.
The child must not have provided more than half of his or her own support for the year.
The child isn’t filing a joint return for the year (unless that joint return is filed only to claim a refund of withheld income
tax or estimated tax paid).

If the child meets the rules to be a qualifying child of more than one person, only one person can actually treat the child as a
qualifying child.

Children of Divorced or Separated Parents (or Parents Who Live Apart)

In most cases, because of the residency test, a child of divorced or separated parents is the qualifying child of the
custodial parent. However, the child will be treated as the qualifying child of the noncustodial parent if the rule for children of divorced or separated parents (or parents wholive apart) (discussed next) applies.

A child will be treated as the qualifying child of his or her noncustodial parent if all four of the following statements are true.
1. The parents:
     a. Are divorced or legally separated under a decree of divorce or separate maintenance,

      b.Are separated under a written separation agree-ment, or
      c.Lived apart at all times during the last 6 months of the year, whether or not they are or were married.
2.The child received over half of his or her support for the year from the parents.
3.The child is in the custody of one or both parents for more than half of the year.

4.Either of the following applies.
a .The custodial parent signs a written declaration, discussed later, that he or she won't claim the child as a dependent for the year, and the noncus-todial parent attaches this written declaration to his or her return. (If the decree or agreement went into effect after 1984, see Divorce decree or sepa-ration agreement that went into effect after 1984 and before 2009, or Post-2008 divorce decree or separation agreement rule).
b. A pre-1985 decree of divorce or separate mainte-nance or written separation agreement that ap-plies to 2018 states that the noncustodial parent can claim the child as a dependent, the decree or agreement wasn’t changed after 1984 to say the noncustodial parent can’t claim the child as a de-pendent, and the noncustodial parent provides at least $600 for the child's support during the year.

Custodial parent and noncustodial parent. The custodial parent is the parent with whom the child lived for the greater number of nights during the year. The other parent is the noncustodial parent.
If the parents divorced or separated during the year and the child lived with both parents before the separa-tion, the custodial parent is the one with whom the child lived for the greater number of nights during the rest of the year.
A child is treated as living with a parent for a night if the child sleeps:
•At that parent's home, whether or not the parent is present, or
•In the company of the parent, when the child doesn’t sleep at a parent's home (for example, the parent and child are on vacation together).

Equal number of nights.

If the child lived with each parent for an equal number of nights during the year, the custodial parent is the parent with the higher adjusted gross income.
December 31.

The night of December 31 is treated as part of the year in which it begins. For example, the night of December 31, 2018, is treated as part of 2018.
Emancipated child.

If a child is emancipated under state law, the child is treated as not living with either pa-rent.
Absences.

If a child wasn’t with either parent on a par-ticular night (because, for example, the child was staying at a friend's house), the child is treated as living with the parent with whom the child normally would have lived for that night, except for the absence. But if it can’t be deter-mined with which parent the child normally would have lived or if the child wouldn’t have lived with either parent that night, the child is treated as not living with either pa-rent that night.

Parent works at night.

If, due to a parent's nighttime work schedule, a child lives for a greater number of days but not nights with the parent who works at night, that pa-rent is treated as the custodial parent. On a school day, the child is treated as living at the primary residence regis-tered with the school.