i was told the way it worked was that the intern really needs to have every opportunity to perform the admission:
1) ideally, the intern should independently see the patient, and the resident sees patient afterwards. if swamped, to save time, the resident sometimes sees the patient together with the intern, but should let the intern lead the interview and examination, and only interject with questions or looking for clinical findings that the resident thought were missed. rarely does the resident see the patient first, unless i.e. intern is at conference and patient really needs to be evaluated, or intern is at clinic. in this case, intern still independently sees patient afterwards.
2) intern should place all admission orders. but again, if intern is preoccupied and patient really needs some orders and has been waiting for a while, resident could place skeleton orders like vitals, fluids, diet, etc. rarely should the resident place significant management orders unless it was absolutely necessary.
3) intern and residents always write separate notes. intern notes should be detailed, and resident notes are kind of like teaching attending notes where it is more summarized and can say "refer to intern note for more details." rarely would a resident write a team note in situations such as extremely busy, multiple codes and rapid responses, etc. and resident is trying to prevent work hours violations or is being really nice especially in the first half of the year.
if you feel that your resident is detracting from your learning experience, you may need to do something about it. if you feel the resident is good but just not used to being a resident and are comfortable with saying it, bring it up with him/her. if not comfortable and want to wait, you could write your concerns in the end of rotation eval. if really concerned, then you'd have to bring it up with either the teaching attending, chiefs, or the PD's depending on what kind of hierarchy there is for stuff like this in your program.