My other cousin on the other side of the family was comp feeding from birth onwards. She would do breast,breast,bottle(formula). Is this a common thing to do and do hospital encourage that if your milk isnt coming in or your baby is really really hungry (Sorry here I go with the boobies again).
It depends on a number of things.
My milk did not come in til day 5, and DS did not attach well.
The oncall paed (who I never saw) wrote him up for comp feeds.
The midwifery staff and the LC's discussed it with me, and we chose to not give them to DS. I kept him with me the entire time. I was expressing (or attempting to) on a hostpial pump every 1.5 hours, and we were feeding this to DS.

It did help that he was 10lb 4oz and his 10% borthweight was a lot more than a small babies would have been.

I was quite comfortable with not giving him the comp feeds.
He was really really hungry. I believe all babies are, and (again my opinion)their cries help your you milke to come in and are a signal to your body
Babies stomachs are so tiny for the first few days, than he could get by on the colostrum and small amounts I was able to express.