I graduated in the last few years and team nursing is all I've ever known. Seems to work pretty well to me - Honestly, I can't picture how it would have worked any other way (In medicine, at least).
Our system works like this:
Each unit typically has 3 teams of 1 RN, 1 LPN and 1 Healthcare Aid (for day shifts, that decreases for eves and nights).
The RN is the lead, but you generally each have your own 5-6 patients, and knowledge about the other 5-6 from report. As the RN you may be expected to do certain tasks on your teammates patients if they are outside their scope (ie for us, LPNs cannot hang blood, TPN and others), typically your buddy will help you pick up the slack on your patients if you are helping them with something.
AM assessments are typically done together on all 10-12 patients, one person assesses, the other records, in some cases the HCA may go on ahead to start vitals. The RNs are generally expected to do the MD calls and check the labs, but it's something that can be discussed between buddies. Routine meds are done by the patient's primary nurse (so you do 'your' 5-6 patients, and your buddy does theirs).
What I like with this model is that you always have a partner in close proximity with at least vague knowledge of the team's patients and you have someone to bounce ideas/thoughts off of. For breaks you alternate off with your buddy and I have, the vast majority of the time, found that my buddy has settled all their patients before leaving, so you may be called on for a PRN or help to mobilize to the washroom or something but you aren't doing full med passes or anything. Its really not as bad as it sounds.
Remember, your buddy is a nurse too and despite being you being the team lead their actions still fall on their license.
The downside with this model (again.. at least for us) is that we no longer have a designated charge nurse. One of the RNs is 'resource' and covers the administrative unit stuff while having a full patient load. There isn't usually much as the team leads are responsible for most 'chargey' type stuff.. but some days it can be hell being resource.