Jeremy Meeks has a super tight grip on his gf Chloe Green ... so tight, it's like she stands to inherit a $5 billion fortune or something.
The ex-con and the Topshop heiress were out in Bev Hills Friday running the typical errands -- drug store run, smoothies and totally 100% authentic, impromptu make out session for the paparazzi.
Jeremy -- who just filed for separation from his wife, Melissa -- told us last week things are getting serious with Chloe.
Lips and hips don't lie.