NBA Star Chris Andersen -- All My Tats Were Free ... 'I'm A Walking Billboard'

More than half his body's covered in tats ... which can cost a FORTUNE ... but NBA stud Chris Andersen tells TMZ Sports he hasn't paid a single cent for any of his artwork.

So, how did Birdman get the low, low price of "on the house" when it comes to his ink?

"I'm a walking billboard," Andersen says.

We're guess what he means is ... tattoo artists LOVE having their work displayed on a 6'10", 245-pound canvas that gets seen by millions and millions of people every week.

Translation -- it pays to be famous ... so you don't have to pay.