§ 1.152-4 "Special rule for a child of divorced or separated parents or parents who live apart" states that :
"(1) In general. Under section 152(e)(1)... a child is treated as the qualifying child or qualifying relative of the noncustodial parent (as defined in paragraph(d) of this section) if the requirements of paragraphs (b)(2) and (b)(3) of this section are met. The requirements of this paragraph (b)(2) are met if the parents of the child provide over one-half of the child's support for the calendar year, the child is in the custody of one OR BOTH parents for more than one-half of the calendar year. As I understand, if a child lived with both parents in total 183 days or more the requirement "more than one-half of the calendar year" is met even if a child lived with one parent 100 days (who is custodial parent because of greater number of days) and with another parent 84 days (who is non custodial parent). So, if for example the child lived 100 days with Grandmother and 100 days with father and 165 days with mother, the total 100+165 days counts as the child was more than half of the year in the custody of both parents. It also could be possible for the parents to have the child exactly the same number of days if the child lived for example with someone else during the part of the year. So, in case with divorced parents the child does not have to live with just one parent 183 days or more, right?
Here is relevant example #4
Example 3.
(i) D and E are the divorced parents of Child. Under a custody decree, Grandmother has the right under state law to physical custody of Child from January 1 to July 31, 2009. (ii) Because D and E do not have the right under state law to physical custody of Child for over one-half of the 2009 calendar year, under paragraph (c) of this section, Child is not in the custody of one or both parents for over one-half of the calendar year. Therefore, section 152(e) and this section do not apply, and whether Child is the qualifying child or qualifying relative of D, E, or Grandmother is determined under section 152(c) or (d).
Example 4.
(i) The facts are the same as in Example 3, except that Grandmother has the right to physical custody of Child from January 1 to March 31, 2009, and, as a result, Child resides with Grandmother during this period. D and E jointly have the right to physical custody of Child from April 1 to December 31, 2009. During this period, Child resides with D for 180 nights and with E for 95 nights. D executes a Form 8332 for 2009 releasing D’s right to claim Child as a dependent for that year, which E attaches to E’s 2009 return. (ii) Under paragraph (c) of this section, Child is in the custody of D and E for over one-half of the calendar year, because D and E have the right under state law to physical custody of Child for over one-half of the calendar year. (iii) Under paragraph (d)(3)(ii) of this section, the nights that Child resides with Grandmother are not allocated to either parent. Child resides with D for a greater number of nights than with E during the calendar year and, under paragraph (d)(1) of this section, D is the custodial parent. (iv) Because the requirements of paragraphs (b)(2) and (3) of this section are met, section 152(e) and this section apply, and E may claim Child as a dependent.
