Steve Nash -- Lakers Star In Dogfight Over Child Support

L.A. Lakers star Steve Nash thinks he has a good reason NOT to pay child support -- if he does, he thinks his ex-wife will spoil the kids with limos and other luxuries.

Nash is locked in a legal war with Alejandra Nash over their 3 kids. She currently lives in Arizona, where a judge handled their divorce and ruled she was not entitled to child support. She's appealing the ruling and we now know what they're arguing over.

Steve convinced the divorce judge -- Alejandra doesn't need child support because he made her a millionaire 5 times over in the divorce settlement. On top of that, she pulls in more than $30k a month.

For her part, Alejandra says Steve makes a million bucks more than her every month, and it's unfair he's not forced to use some of it for the benefit of their kids.

Steve is saying he's paying plenty -- 90% of medical, school and extracurricular activities, and 82% of the nanny's $2k a month salary. He says he's worried if he pays more, she's an excessive spender who will spoil and damage the kids with crazy luxuries.

But there's more going on here. As we previously reported ... Alejandra wants to move to L.A. but Steve is objecting. It's really weird, because the b-baller has said he chose to go to the Lakers rather than the Knicks so he could be closer to his kids.