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Tom Brady heard 198 names before his in 2000 ... but his niece, Maya , didn't have to wait at all to have hers called on Monday -- 'cause the former UCLA star went No. 1 overall!!

The Athletes Unlimited Softball League held its expansion draft as it grows to six teams before next season ... and the Oklahoma City Spark had first dibs on a handful of unprotected players from the original four franchises.

Brady previously suited up for the Talons after going 19th overall in the draft earlier this year ... and went on to hit .647 with a homer and five RBI in six games to help her squad win a championship.

That's all the Spark needed to see ... 'cause Brady was first off the board with the top pick. Gallery Launch Gallery Getty

Of course, Brady's uncle famously f

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