COLUMBIA — Tyrone Joel smiled, revealing a mouth full of bloody gauze, as he strolled out of the Cantey Building at the State Fairgrounds on Friday morning.

“I’m very thankful for this,” said Joel, 52, of Columbia. “I wish I could hug everyone here.”

Hugging every volunteer at SC Mission 2012 and the S.C. Dental Association Dental Access Days might have taken all day. So many people wanted to help provide free health care for the uninsured and underinsured that organizers had to turn away volunteers.

The dental effort in the Cantey Building was the busiest section, an indication of how many people don’t have dental insurance. Before the gates opened at about 5:30 a.m., the line for dental care stretched completely across the huge fairgrounds parking lot.

There were more than enough dentists and dental hygienists to keep patients flowing through 80 dental chairs, but those at the end of the line likely faced waits as long as 12 hours before getting care.

That’s better than last year, however, when logistical problems at the first SC Mission in the Midlands at Carolina Coliseum frustrated those seeking care and those hoping to help them. Some people waited for hours in the heat last year and never got the dental or eye care they were seeking.

This year, the system worked better. Lines were separated for medical, dental and eye care. People got numbered armbands as they came through the entrance and waited in air-conditioned tents. (The tents grew warm late in the afternoon.) Organizers also had a better idea of how many people they could treat.

“The experience for everybody, and particularly for patients, has been extremely positive,” said John Kessler, vice president of marketing and business development at Providence Hospitals and chairman of the event’s steering committee. “People are getting through faster.”

Dental officials planned to treat about 900 patients by the time the program was shut down at 6 p.m. Friday. Those who couldn’t be seen Friday would be given vouchers to put them at the front of the line today, when the effort continues from 6 a.m.-3 p.m. Another 600 should be able to get dental care today.

Eye care, with fewer work stations and volunteers, had only about 220 openings Friday, and all were filled by 10:30 a.m. Capacity actually exceeded demand for general medical care Friday.

As of 4 p.m., the effort was surpassing its goals, with 1,024 dental patients, 229 eye care patients and 338 medical patients.

Joel was one of the first patients to exit the dental section. While pushing his rolling oxygen tank, he said that he recently had been put on federal disability. But Medicaid covered only medical care, not dental. And he sorely needed dental care.

“I had eight teeth pulled,” he said as best he could.

Joel was among about 50 people pre-screened through local churches and given preliminary dental exams on Thursday. That way, the dentists had patients ready for work as soon as they arrived Friday.

Inside the fairgrounds, Dr. Lee Ayers gathered the dental workers for a cross between an operation prep and a pep talk at about 6 a.m.

Don’t worry about the little things, he told the group. “There already have been more snafus than you can imagine,” he said. “Our objective is to keep going and keep going and then, at 3 o’clock Saturday afternoon, we will have helped 2,000 people.”

Despite the crowds waiting for dental help, organizers said fewer than expected had shown up.

At the group’s Dental Access Days in Florence last summer, they had to turn away about 2,000 people.

Volunteers carried yellow signs shaped like teeth on a stick, with letters designating extraction (X), surgery (S), filling (F) or cleaning (C). When a chair for one of those procedures opened, the volunteer would walk to the waiting area, hold up the sign and call the next person in that line for that procedure. Seldom did a dental chair get cold before another patient sat down.

The lines were shorter in the medical care area. Doris Williams, 59, of West Columbia, arrived in the parking lot about 2 a.m. By 7:30 she was the first to file out of the medical section, with medications for her high blood pressure.

The wait was slightly longer at the eye care area. Jennifer Smith, 27, of Columbia, was walking out about 8 a.m. with a prescription for badly needed glasses. (She had to come back later in the day to get her glasses.) She had been frustrated by people cutting in line in the parking area during the night, but as she left with her 7-month-old son Jacob, she said: “I am so happy. After all this, it was worth it.”

The two-day event is a project of many of the local health care organizations to help the nearly 20 percent of South Carolinians without health insurance. Many more people are underinsured for medical care or have no dental or optical insurance.

As patients left, they were given information on what free or discounted care is offered year-round in the area. It’s limited for dental and eye care, but there are several free or low-cost medical clinics.