Shared physical custody is uncommon, the standard being primary physical custody with one parent. You also may wish to get to Court before she files in Maine and save yourself some trouble down the road.
You really should talk to an attorney as to what the expectations, duties and benefits of your options.
I actually see shared physical custody becoming more and more common. However, this generally only works when the parents live close enough to each other that it is logistically possible and reasonable for the child involved. Unless you two reach an agreement, the question presented to the Court will be what is in the child's best interest (your ex girlfriend doesn't get to make this decision herself).
I would strongly recommend that you speak to an attorney now about the process, when you should be filing, etc. I would also recommend that you speak to someone local who is licensed in both Maine and New Hampshire and can discuss the options regarding jurisdiction (where to file). On a related issue, to avoid any risk that the child will be placed for adoption without your knowledge, you can register with the New Hampshire putative father registry (I do not believe Maine has a similar registry, but you should speak with an attorney in Maine that handles these types of issues to confirm this).
Too bad that the drama has already begun. Consult with a family lawyer now to ensure matters have been. It may be a bit to premature, but you still need to consult with a family law lawyer who does work in in both states (if the state line is nearby).
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