Tyga: Expensive Pet Tiger Ain't MY Problem Now

Tyga is nothing but a deadbeat dad to the tiger he illegally owned ... at least in the eyes of the sanctuary that's now racking up HUGE costs to care for the animal.

The big cat's now called Maverick and it's living at Lions, Tigers & Bears non-profit rescue in So Cal, but the staff tells us Tyga's never made any effort to help out with his care.

Founder and director Bobbi Brink tells TMZ ... it costs more than $10k a year just to feed a 500lb tiger like Maverick, plus there are vet costs, flea control and general maintenance. She says they rely on public donations to cover costs.

We're told the rapper hasn't so much as said thanks to the facility. You'll recall, Tyga faced criminal charges for having the exotic pet. He eventually surrendered it to animal control, which transferred the tiger to LT&B.

Law enforcement tells us Tyga effectively dodged the charges because they couldn't track him down when he moved. The good news ... Maverick looks like he's doing just fine.