Legal Question in Landlord & Tenant Law in Massachusetts

The lease is a contract between you and the landlord and not between you and your ex. You are each 100% responsible for the entire rent. The landlord does not care who pays just that the full amount is paid. If the landlord evicts for non payment he will sue both of you for the full amount owed.

Now that I have the restraining order is he automatically off the lease? No. Your landlord can have you sign a new lease with only your name if he wanted but it does not change the rental amount.

He does not give me any money (currently going to probate to try for child support). You definitely need to seek the child support payments. You could have asked the judge who issued the restraining order for such support.

Am I legally responsible for the $700 rent each month myself even though I have the order? Yes

I would assume I am only responsible for $350. Incorrect.

And can I ask probate to have him help pay for the rent even though he doesn't live here any more? You can ask but they will likely only obligate him for child support based on your respective income.

You and he are responsible for the $700 rent under the terms of the lease, but if he does not pay and you want to stay there, you need to pay the rent.

Probate court will set his child support requirements based on both of your incomes. You can ask for them to consider the cost of the housing for $350 per month as well, but the court will base the child support based on his income and yours. If he has medical insurance through work, he should cover the child as well unless you cover the child on your medical insurance.