Bobbi Kristina -- Nick Gordon Sued ... He Robbed Her Blind and Beat Her

Bobbi Kristina was the victim of a nefarious plot by her boyfriend Nick Gordon, who secretly stole cash from her Whitney Houston inheritance, and physically abused her ... according to Bobbi's conservator.

Bobbi Kristina's estate filed a $40 million lawsuit against Gordon on Wednesday ... accusing Gordon of regularly transferring funds from her account to his account, including $11,000 AFTER she'd fallen into the coma.

The docs also say Gordon was beating Bobbi Kristina, and on one occasion dragged "her upstairs by her hair." He also allegedly punched her in the face and knocked out a front tooth.

Bobbi Kristina intended to reveal the abuse she was suffering to a close friend. According to the docs, she had set up a time to meet that friend on Jan. 31 ... but she never made it.

Instead, Bobbi Kristina was found face down in her bathtub that morning with a swollen mouth and another tooth knocked out. The lawsuit doesn't squarely blame Gordon for those injuries, but it strongly hints at it -- and as we've reported ... police have been investigating Nick.