i am sorry you and your boyfriend are going through such a painful and difficult situation

every situation is different, and of course as you mentioned some laws on divorce and child custody may vary, state to state.

most state divorce and custody laws are outlined in numerous books in your local public library. and. . . . online. you can get actual copies of the LAW though, at your library. both would be a good start. (note. fathers have rights. there are attorney's who specialize in fathers rights)

my personal opinion on how you can be supportive and helpful to him at this hugely difficult time, is to remain loving, but keep in mind if he seems distant or needs space, that it is not personal towards you. it is often how a man needs to work through things.

you can also help by beginning this legal research, and then when he seems receptive tell him you felt if you got some information it would take some pressure away from his own stresses and duties. . . and no matter what he decides, extra knowledge can ONLY be a bonus.

and lastly, but certainly not the least important, stand by him, no matter what the outcome or what decision he makes. he needs your approval though he won't outwardly ask for it. these are likely the most difficult decisions he'll ever make in his life, and in all honesty, they are his to make, and the mother of the children. and the court. you take a secondary role, but please don't think i mean that in a disrespectful way.
you may take a secondary role in the decision making process, but you can take a primary role in his life and heart if he knows you are there no matter what. and that you believe in him

thanks for letting me 'chime in'.
and i wish you and your bf the very best.