The wisdom of Solomon: splitting up with animals

I seem to recall -- and I am resisting the siren song of Google to dig into it and find research! -- that in the Bible there's a famous story about King Solomon and his wisdom in solving challenges and arguments brought before him.

The specific story I'm thinking about revolves around two women who came before the King, continuing their heated argument about who should have possession of a baby: both had given birth, one baby had died, and they each claimed ownership of the surviving baby. They couldn't agree, they didn't want to "share" the baby and they appealed to the wise king for a solution.

Apocryphally, King Solomon asked one of the guards for a sword and stopped, poised, ready to cut the baby down the middle, to the horror of all in the court.

The bickering women stopped and stared, but Solomon said "this is the best and most fair solution to your argument of who should have the baby, but the price might be more than you're willing to pay."

I am wondering how applicable that is to family pets when a couple breaks up. I'm more of a cat person than a dog person, truth be told, so I'm definitely not proverbially standing in Solomon's court claiming co-ownership of our dogs, but the cat, well, that's another story.

Newton has been with our family for almost two years and has spent far more time with me than anyone else, particularly when I would stay up late into the evening reading, watching movies or working. My constant companion, we're good buddies.

When Linda and I split households almost six months ago, he stayed with her because I initially wanted to be free of all pet responsibilities as I set up my new pad. Ten days ago, however, Linda flew out to Europe on a trip and I've been cat-sitting Newton and helping nurse him back to health (he had a serious eating disorder and needed daily medicine, feeding through a catheter, etc).

He's in great shape now and the last week and a half have been a great chance to reconnect with him, and he seems to really love my place. In fact, the kids have nicknamed him "Thunderpaws" because of his constant racing through the house, up the stairs, over the couches, etc.

My question: who should have the cat? Should he go back to Linda's place when she returns from her trip, to share space with two dogs, two hamsters and such, or should he stay with me and bring positive cat energy to my household? Needless to say, I'd rather avoid the "sword solution" if possible!

This also brings up a general question about how do you fairly separate out family pets when you separate / divorce? I have heard a few stories of shared custody where a dog will be with one "parent" for weeks or months, then switch, but even more than with kids, that seems like a terrible idea. So... what's your recommendation?