Can my spouse come after my house if its in ny name only?

Upon divorce, the court will divide all assets. This includes assets held in only one parties' name  The laws presumes the assets will be divided equally but the court may awarded one spouse more assets than the other spouse depending on various factors. So, depending on the facts of your case, the court may or may not award her an interest in the house but the presumption will be she gets one-half.