California is changing up the way it is delivering coronavirus vaccines, moving to a more centralized system that is expected to streamline appointment sign-up, notification, and eligibility for nearly 40 million residents who want to know when they can get a shot and where.

But the administration of Gov. Gavin Newsom provided few details Tuesday. Counties, which have been leading the vaccine effort along with hospital and health care systems, were cautious about what to expect and said they need more information.

California has been criticized for vaccinating so few people even amid a national vaccine shortage that appears to be the main bottleneck, administering about 2.6 million of 4.7 million doses shipped. At the same time, confused residents are clamoring for more information and frustrated by eligibility rules that vary by county and by hospital system.

Newsom announced Tuesday that unnamed private third-party administrators will work with a new statewide secretary in charge of delivery to decide where the state’s supply of vaccine should go as federal supply ramps up to meet demand. A new sign-up tool will also allow the state to better track where vaccines have gone and who has been vaccinated, while also allowing residents to schedule an appointment when it’s their turn.

The state will move to an age-based eligibility system that should make counties and hospital networks — which have been scheduling appointments and determining eligibility under broad state guidance — move at a more uniform clip. Currently, some counties and hospital systems are taking appointments for people 65 and older while others are limited to 75 and up.

Counties say they welcome change if that means more clarity and information, but also warned that local governments are the eyes on the ground that ensure vulnerable populations — including people without insurance or in hard-hit communities — are inoculated.

“We would see this change moving from a system that was not working, that was piecemeal in structure, to a new system that could work, if it is structured carefully and doesn’t risk those populations that we’re most trying to protect,” said Graham Knaus, executive director of the California State Association of Counties.

But the news was not welcomed in the Silicon Valley county of Santa Clara, where county executive Dr. Jeff Smith said he has been “trying to decipher press releases and announcements” to figure out what will happen. The county is among those pleading for more vaccine, saying they are limited only by supply.

“That really, really fries me,” Supervisor Mike Wasserman said. “Sacramento’s being stupid by taking away something that we’re doing and thinking they can do it better.”

Fresno County requested 38,000 doses this week but only got 12,000, and the shortage has led the county to temporarily limit operations to 1.5 days from six days a week at its largest vaccination site, said Joe Prado, the community health division manager.

“I think any response when you bring in additional resources, that is a plus,” he said. “But if you don’t coordinate well and you don’t really get a focused plan together in line with the locals, then it can become inefficient.”

Yolanda Richardson, newly appointed secretary of the government operations agency, said at a Tuesday briefing that this new system is “about California being prepared to make sure that we can get out the vaccine when more supply is available” and emphasized that counties will continue to play a role in delivering doses equitably.

The third party administrator or administrators will allocate vaccines directly to providers, which will include public and private health systems, pharmacies, hospitals, community health centers and mobile sites, she said.

The state has launched a website called “My Turn” where people can sign up to be notified when they are eligible for a vaccine and to schedule appointments. The website would also eliminate the need for counties to maintain their own registries.

It’s unclear how a new system will affect giant vaccination sites like Los Angeles’ Dodger Stadium and Orange County’s Disneyland, which have been inoculating thousands of people a day and to a much broader group of people.

Teri Perlstein, who set up the Facebook group VaxMe OC to help frustrated residents navigate Orange County’s vaccine registration site, said more consistency is sorely needed. She said she has been fielding questions from teachers about whether they can drive up to the Los Angeles County city of Long Beach to seek a vaccination sooner than they’ll be able to get one in Orange County.

“I don’t think it’s fair to have it inconsistent depending on what side of the line you live on,” she said.

With the latest announcement, Perlstein said many questions remain about the state’s plan, including whether it will affect residents who got their first shot and are waiting on their second. She also asked what paperwork essential workers would need to present to get a vaccine from the state.

Right now, the biggest issue for residents “is the lack of real communication,” she said.

California has said health care, education and child care, emergency service and food and agriculture workers, as well as anyone 65 and older, are eligible for vaccines. But after that, eligibility will be based on age, drawing complaints from transit and other industries.

Dr. Charles Bailey, medical director for infection prevention at Providence Mission Hospital and Providence St. Joseph Hospital in Orange County, welcomed the change. He said hospitals were equipped to vaccinate their own workers, but that’s on a much smaller scale than what’s required to roll out the vaccine to the general public.

He also said that simplifying requirements also makes the process easier, and advanced age is the biggest risk factor beyond any other underlying conditions. Allowing the state to seek an equitable distribution of the vaccine will allow counties to focus on getting as many people inoculated as possible.

“It will alleviate the counties from having to defend decisions, which obviously they don’t need to spend time doing that,” he said.