Bravo's Greg Plitt -- Had $800K in the Bank ... But No Will

Bravo's fitness star Greg Plitt -- who was hit and killed by a commuter train -- did not have a will, and now his family is trying to ensure his $800,000 estate ends up in the right hands.

As TMZ first reported ... Plitt died tragically in January while shooting a commercial for a sports drink.

The 37-year-old did not have a spouse or child when he died -- and according to court docs obtained by TMZ ... his father filed a petition Wednesday to control his son's estate.

If approved -- which is extremely likely -- he'll make all decisions about paying Greg's creditors ... and how the remaining money gets divvied up.