Tamar Braxton Divorce, Our Kid Should Live with Me

Tamar Braxton isn't into sharing when it comes to custody of her son ... TMZ has learned.

We broke the story ... Tamar filed for divorce from Vincent Herbert, citing irreconcilable differences. We now have the divorce docs, in which she wants full physical custody of 4-year-old Logan.

It sounds like there's no love lost here. Tamar also wants the judge to turn thumbs-down if Vincent asks for spousal support.

As for assets, Tamar lists one big-ticket item ... their house in Kardashianland ... aka Calabasas. She acknowledges the house is community property. There is no evidence of a prenup.