The will always give an - woman Anti D (with her consent of course, you can refuse this, as it is a blood product and hence comes with all the -minimal- risk of other blood products)

They wont ask what your partner is (if you know), because they can never be sure that they were the father.

DH is +, and hence i have anti D, but if he was - (hence my baby must be neg), and i was sure he was the father, i would refuse to have it.

The main problem is with subsquent preganancies, because the time when blood mixing (and hence antibody formation), occurs is at birth. It can also happen with m/c or a knock to the stomach, so you should make sure if these occur to talk to your dr about having Anti-D.

There is a book against Anti-D "Anti-D in midwifery", i don't buy the arguments in there personally, but it is worth the read.