George Zimmerman -- Busted for Epic Art War With GF

George Zimmerman allegedly hurled a wine bottle at his gf's head because they got into a heated convo about a work of art.

As we told you ... Zimmerman was arrested over the weekend, and according to the police report -- obtained by TMZ -- the alleged domestic incident started on Jan. 5 when Zimmerman and the woman were talking smack over a painting he wanted back from her.

Cops say the woman got pissed, started to walk out ... and then George tossed the bottle, which missed her and hit his garage door.

Zimmerman's been dabbling in painting himself ... though it's unclear from the report if it was an OG Zim piece that started the fight.

Police spoke to Zimmerman about the fight on Jan. 9 -- and he claimed SHE threw the bottle. Cops didn't buy his version of the incident ... and arrested him for aggravated assault.