Go talk to a local divorce attorney and get ALL your questions answered. You should not be paying 1/2 the bills at the apartment you left. Of course if you can get your name off the lease do so.
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Generally, when you file for a divorce, the parties have to pay for their own things. If you have two different places to live, you don't pay for his apartment. Absent a situation where you are ordered temporary spousal support, if both parties can support themselves, they pay for their own expenses. And until you get a court order saying you owe temporary spousal support, you don't owe anything.
I'd still sit down with a local attorney to discuss your options (or at least review the paperwork).
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