Who Will Take the Kids?

Standard Dom Com plot in which parents ponder over who will take custody of their children should some tragedy befall them. This can play out in a number of ways:

If there are multiple candidates, they will jealously compete with one another and attempt to curry the parents' favor, not unlike a political campaign;
If the show features a Goofball or Straw Loser, this one will be summarily ruled out from the outset. Expect this character to enact a Zany Scheme in an attempt to prove his/her worthiness, only for it to bomb spectacularly. Only, it doesn't bomb, really; despite the apparent failure, the scheme will actually prove that the character cares deeply about the children... which is what the parents were looking for all along.
For added comedy value, the person(s) ultimately selected may not want the job.

Not to be confused with Taking the Kids.

Examples of Who Will Take the Kids? include:

Everybody Loves Raymond: Both sets of grandparents are ruled out (Debra's parents because her father drinks a lot, Ray's parents because—they're Ray's parents). The couple they eventually choose declines the honor because they don't want to deal with Frank and Marie.
Yes, Dear
Two and A Half Men
Roseanne
Home Improvement
Friends
Malcolm in the Middle
In Mad About You, they agonize over selecting the godparents.
In Big Love, the situation is accentuated in both seriousness and hilarity because the marriage in question is polygamous. Legally speaking, it's impossible to predict who would get the kids without clear, explicit instructions.
In Kevin and Kell, the title couple went through every relative they could think of as a possible guardian for Coney, and finally settled on Lindesfarne, who was then still in high school (she recently graduated from college and got married), but was still deemed the most level-headed, mature, reliable candidate available at the time. This arc starts at this strip and continues through that week.
This happens in one episode of the Animated Adaptation of Baby Blues.
The aversion of this is what kicks off A Series of Unfortunate Events. Rather than name a guardian for their children, the Baudelaires decide that they should go to any person their executor feels like assigning them to, so long as they are somehow related. Rather than carefully considering who would be the best choice for this task, said guardian chooses their absurdly distant cousin Count Olaf (who they've never even heard of before) on the grounds that his house is on the way to the train station, which enables him to drop them off on the way to work without disrupting his schedule.
The conclusion of this trope is the basis of the 2010 film Life As We Know It.