At the hospital where I'm a PICU fellow we have a separate CVICU (for all of the post and sometimes pre-op congenital hearts) and PICU (for everything else).
The CVICU is run by either a dually trained peds cardiac intensivist or a PICU attending with a cards attending also there to lend their expertise. Some, but not all, major management decisions are also run by the surgeon who did the case. Or at least we try to keep them in the loop. Post-op admit orders are written by both the surgeons and the medical team, each focused on obviously surgical or medical issues. However afterwards, the care of the patient is primarily under the medical team.
The PICU manages all the patients, whether they be post-ops, traumas, etc. with the specialists consulting. They will sometimes write the admit orders but after that they are under our care. Often they will write specific orders for their patients but that is with the understanding that they'll notify us what they are, and that we ultimately have final say if we disapprove.
I did my residency at a different program. There was no distinction between CVICU and PICU per se, but given the size of the unit there were several distinct teams: 1. an essentially CVICU team consisting of a PICU attending, fellow and nurse practioners, who would round with cardiology, 2. a hospitalist/NP team with a PICU attending and +/- a fellow at the head, and 3. a resident team consisting of a PICU attending, fellow, and obviously residents. There the ICU teams wrote all the orders, admit and all. The only exception was neurosurgery, who could write orders, but again, only if discussed with the ICU team.