Kim just filed legal docs, obtained by TMZ, asking a judge to grant a restraining order against Melvin Jeffery Conley. According to the docs, Kim got a call from Emma, warning her a man who had broken into Emma's house told her about his desire to make contact with Kim and her kids.

Back in May, Conley allegedly broke into Emma's house and used her landline to dial her cell phone. Emma missed the call but saw someone was calling from her landline ... she figured it was a family member so she called back and Conley answered. He claimed Emma gave him permission to stay at her home ... she did not.

The next day, Conley showed up at Kris Jenner's house and told security he thought he was at Kim's house and he was her "long-time manager" and a player with the Toronto Raptors. He said he had an appointment to meet her that day.

Last month, Conley showed up at Kim's Malibu home, where he was confronted by security along the perimeter fence. He told security he was going to jump the fence ... but that effort was thwarted.

Kim says in legal docs her Malibu home is not easy to find nor publicized and it shows the lengths he is willing to go to make contact with her and her kids.

She says Conley has caused her "worry, concern and severe emotional distress."

As for Emma, she obtained a 5-year restraining order against Conley.