When Luke Adami, 6, sustained a gash to his chin on a playground, his parents rushed him to an emergency room at an in-network facility, Valley Hospital in New Jersey. The parents, Greg and Madeleine Adami, asked about a plastic surgeon to sew him up. Mr. Adami recalled: “You go to a hospital that’s in-network, your kid’s bleeding. What are you going to say?”

The nurse did not mention that the surgeon she called was out-of-network and would charge a separate fee. Neither did the plastic surgeon say anything about costs when he came in.

The surgeon billed the Adamis $4,878 for eight stitches that were coded as “open wound, jaw, complicated.” “When I looked at the bill, I laughed and I told the surgeon’s office, ‘Process this claim with my insurer. I’m not paying out-of- pocket,’  Mr. Adami said. “The hospital has control over who they bring in. But I do not.”

Patients have no choice about which physician they see when they go to an emergency room, even if they have the presence of mind to visit a hospital that is in their insurance network. In the piles of forms that patients sign in those chaotic first moments is often an acknowledgment that they understand some providers may be out-of-network.

But even the most basic visits with emergency room physicians and other doctors called in to consult are increasingly leaving patients with hefty bills. More and more, doctors who work in emergency rooms are private contractors who are out-of-network or do not accept any insurance plans.

While patients have complained of surprise out-of-network charges in hospitals from some other specialists — particularly anesthesiologists, radiologists and pathologists — the situation with emergency room doctors is even more troubling, patient advocates say. For one thing, patients cannot be expected to review provider networks in a crisis, and the information to do so is usually not readily available anyway.

When emergency medicine emerged as a specialty in the 1980s, almost all E.R. doctors were hospital employees who typically did not bill separately for their services. Today, 65 percent of hospitals contract out that function. And some emergency medicine staffing groups — many serve a large number of hospitals, either nationally or locally — opt out of all insurance plans.

As more insurance plans contract with narrower networks of doctors to form offerings tailored to the Affordable Care Act, insurers have acquired greater leverage in cutting payments to physicians. While an insurer would have little power to drive a hard bargain with a major hospital that the company needs in its network, it can often pick and choose among physicians, excluding some or offering rates so low that many doctors say their practices are unsustainable.

Dr. Jeffrey Bettinger, chairman of the reimbursement committee of the American College of Emergency Physicians, said that out-of-network emergency room doctors were an unusual phenomenon and expressed doubt that the practice was widespread. When it occurred, he added, it was typically because of insurers’ unwillingness to pay doctors a reasonable rate compare to what they pay hospitals for their services.

Hospital charges for emergency care vary widely. A recent study found that hospital charges for a visit involving a serious medical issue in California varied between $275 and $6,662, just for the facility fee. “Much of the variation we observe may in fact be entirely random,” wrote the authors, emergency physicians at the University of California San Francisco Medical Center. But that variation often does not directly affect patients, since most hospitals participate in the big insurance plans in their area, and patients tend to know which are in their network, so the insurer covers most of the bill.

But it is a different matter with emergency room doctors who bill out-of-network fees, experts say.

When Dr. Michael Schwartz’s daughter went to an emergency room in the Philadelphia suburbs for a reaction to a medication in 2010, she went to an in-network hospital, Bryn Mawr. She was there for a few hours on a cardiac monitor. While most of her care was covered by his family’s insurer, Capital Blue Cross, a bill of more than $2,000 from the out-of-network E.R. physicians for cardiac monitoring was not.

“I tried to negotiate with the physician group, but they wouldn’t budge,” said Dr. Schwartz, a pediatrician, who ended up paying $1,200, the amount his plan required for his share of out-of-network care. “It was ridiculous. I’m a physician and I understand how this works. There was no sign saying, ‘Our physicians are out-of-network.’

Emergency physicians say they are not to blame. “In general, E.R. physicians try to align themselves with whatever networks their hospitals are in, but sometimes the rates pale compared to what is offered to the hospitals,” said Dr. Bettinger of the emergency physicians’ group. That often leads to protracted negotiations, he said, but eventually the insurers and the doctors come to agreement and sign a contract.

In the meantime, patients are stuck with out-of-pocket charges. Regulations created by the Affordable Care Act specify that insurers must use the best-paying among three methods for reimbursing out-of-network physicians dispensing emergency care: pay the Medicare rate; pay the median in-network amount for the service; or apply the usual formula they use to determine out-of-network reimbursement, which often depends on “usual and customary rates” in the area.

But in most states, doctors can then bill patients for the difference between their charge and what the insurer paid.