Dodgers Star Carl Crawford to Baby Mama -- STAY THE HELL OUT OF L.A.

L.A. Dodgers star Carl Crawford is in a nasty custody war with one of his baby mamas ... and it's gotten so bad, he's begging a judge to BLOCK her from moving to California ... TMZ Sports has learned.

We know ... the Dodgers' $142 million man is fighting with Amy Freeman -- the mother of his 9-year-old son and 5-month-old daughter.

FYI -- Crawford's new lady Evelyn Lozada is currently 6-months pregnant with Carl's unborn child ... so, yeah ... do the math on that one.

Anyway, according to legal docs obtained by TMZ Sports, Carl claims Amy has lived in Arizona for the past 12 years where she's been raising the two kids and everything was fine ... until October.

That's when, Carl claims, Amy suddenly packed up and moved out west ... pulling the 9-year-old out of school and putting the family home up for sale.

In the legal docs, Carl says Amy insists she's making the move because she wants the kids to be closer to their dad.

But Carl's calling BS ... claiming she only went to Cali to take advantage of the more favorable child support laws. Translation -- Carl thinks she's only after his money.

Now, Carl is asking the judge to stop Amy from relocating ... the same way Steve Nash tried to block his ex from moving to L.A. after he left the Phoenix Suns for the Lakers.