With Olivia, I cuddled her for around an hour and attemoted a BF, then the midwife and my OB did checks on her (still in the birthing suite, right next to me). Then they offered me a shower and I realised how desparate I was for one, so I hopped int eh shower whilst DH snuggled up with Olivia.

With both Charlie and Lexie (who were both born in the same hospital, Olivia was born in a different one) I BF'd them both before the cord was even cut and snuggled for ages. Then DH cut the cord, then they had their checks. Once I had them wrapped up and comfy with DH we moved from the birthing suite to our room, where I had a shower, DH unpacked for me, whilst bubs slept soundly in the little bassinet thingo.

Depending on which hospital you are in, you can try and dictate what happens. My advice would be, if you can, and in light of the risk of "pass the parcel", stay in the delivery suite as long as you can!!