Steve Nash's Ex-Wife -- He's Banning Me From L.A. to Avoid Child Support

Steve Nash is making a full-court press to block his ex-wife from moving from Phoenix to L.A. with their 3 kids so he can avoid paying child support ... this according to court docs filed by his ex.

Nash and his ex Alejandra are locked in a legal battle royale over where she's allowed to move. Alejandra wants to relocate from Phoenix to L.A. ... so the kids can be closer to Steve. But the b-baller has vigorously tried to block the move, which is curious because he famously chose the Lakers over the New York Knicks to be closer to the youngins.

Alejandra says Nash has told her he didn't want her to move out West because he might be traded or forced into retirement ... which would mean uprooting the family again.

But Alejandra says Nash is simply blowing smoke -- and that the REAL reason he wants her to stay put in PHX is because California courts are likely to impose huge child support obligations against him -- something the Phoenix courts have not done.

Alejandra claims Steve is not paying a cent in child support ... zip, zero, zilch ... and he doesn't want to blow a good thing.

Alejandra says Steve's admitted that living so far from the kids is tough on him and them ... and it would be better for everyone if they could spend more time together ... but his desire to save a few bucks on child support is trumping his obligation to his family.