Yeah, definitely don't feed the troll.
While I think it's amazing that he wants this level of involvement with his daughter, and that he wants to be such a major part of her life, you could decide that you do want to be the primary parent, and want your daughter to spend the majority of her days and nights with you...my opinion is that if that does happen, he should support it, and maximize what time he does get with her in any way possible. 50/50 is a nice split, but it does mean a lot of bouncing your daughter in between two different homes, which can be a lot of transitioning for an infant/toddler/small child. On the other hand, if it happens from the get-go, your daughter won't know any differently, and it could be fine. It's just some things to think about. One major thing impacting your decision early on, is if you're planning to breastfeed your daughter vs. formula feed her. If you intend (or want to try) breastfeeding, she will have to spend the majority of time with you in the beginning, while you're establishing your supply...you could pump, of course, but you'll need that baby close by to latch frequently in the beginning so that you can get a good supply of milk going. If you want to skip that, and go right to formula, then it won't matter so much which one of you has her. Just something to think about!
Also, it would help if you BOTH had all of the necessary supplies at both of your homes, if you're going to do 50/50, such as you BOTH having your own cribs, swings, bouncy seats, you'll both need carseats, your own stash of clothes. It will be far less that both of you have to tote back and forth...sometimes leaving the house with a baby can feel like you have to bring half the house with you! My suggestion would be to save yourselves some grief, and both have everything of your own for your respective homes, so that you don't have to pack and drag it all with you when you switch hands.
How are you doing on supplies, by the way? Now that you know that you want to be a part of the baby's life, have you started shopping a bit for her?