parallel parenting
n. A form of parenting in which a divorced couple assume or are assigned specific parental duties while minimizing or eliminating contact with each other.
Examples
2003
In the most high-conflict cases, the arrangements are being called "parallel parenting" — the idea that with the right contract to guide them, both mom and dad can care for their children independently, without ever having to exchange a friendly word.

Last year, family lawyer Nathalie Boutet represented the mother in an Ottawa case involving a three-year-old girl. A social worker had determined that both parents were important in the child's life, and she would do well with either one of them.

The judge returned with a decision that ordered the parents to share time with their daughter almost equally, but split up the decision making, giving sole responsibility for health decisions to the mother, and charge of education decisions to the father.

Critics of parallel parenting say it is impossible to divide up the decisions of a child's life without overlap; what happens when a Catholic parent, with control of religious decision, wants their child in a Catholic school, but the other parent decides matters involving education?
—Erin Anderssen, “Fine-print parenting,” The Globe and Mail, August 02, 2003
1999
Shared parenting is only considered an option when the parents get along—ignoring the cases of parallel parenting that are trickling down through the courts. (Parallel parenting is where each parent makes all the decisions and does all the parenting when the kids are with them; schedules are usually close to 50/50 and laid out in great detail, and contact between the parties is minimal—and these arrangements seem to work.)
—Jason Bouchard, “The Divorce Survival Kit,” Everyman: A Men's Journal, October 31, 1999
1982 (earliest)
Dr. Furstenberg said he had no quarrel with the Wisconsin group's conclusions about friendly relationships between former spouses, but believed that other sorts of relationships might be more prevalent.

''It seems to me that the predominant mode when formerly married people are parenting is not co-parenting,'' he said, ''but 'parallel parenting'," where each parent operates as a self-contained unit.
—Glenn Collins, “Some broken families retain many bonds,” The New York Times, December 20, 1982
Notes
Although some divorced couples seem to have hit upon parallel parenting arrangements themselves, this two-track parenting scheme is usually court mandated or part of the couple's separation agreement. It is often part of a parenting plan (1988) in which the responsibilities and duties of each parent are spelled out in writing. In case of disputes, a parenting coordinator (2001) is assigned to iron things out.