Amid a years-long slowdown in California's population growth, the Bay Area has emerged as the state's fastest-growing region, even if no one region is gaining people all that quickly.

"California is almost just standing still," said demographer Daniel Sheya of the state Department of Finance, which released its annual population estimates Tuesday.

California grew by 0.67 percent since 2011 to reach 37,679,000 people, while the nine-county Bay Area grew by 0.85 percent, he said. Some 7,249,563 people live here now.

"I think what we see is the revitalization of the Silicon Valley and, along with that, some population draw," Sheya said. "Other than that, there doesn't seem to be much population growth in California."

San Jose gained 14,000 people to reach a population of 971,372. That contrasts with previous state estimates that pegged California's third-biggest city as reaching 1 million people at the end of the last decade.

State demographers revised their estimates after the 2010 federal census found a lower population.

"They found many more vacant units within San Jose than we may have been estimating," Sheya said.

Fremont, Hayward, San Ramon, Oakley, Gilroy, Pittsburg and Sunnyvale were among the fastest-growing Bay Area cities. Morgan Hill was the fastest, growing by 2.3 percent to 39,127, followed by two cities near the San Francisco International Airport: Millbrae and San Bruno.

"We have consistently had, except for a few of the darkest years during the recession, a 2 percent growth rate," said Morgan Hill City Manager Ed Tewes.

The Santa Clara County suburb has added about 200 houses each year, many of them attracting families with kids, he said.

San Bruno Mayor Jim Ruane said proximity to the airport and technology jobs kept his compact city growing with a mix of single-family homes and high-density housing near the BART and Caltrain stations.

"We don't have a whole lot of room to expand. We're pretty much built out. But people are always taking advantage of remodeling new homes," Ruane said.

In the year after the deadly 2010 San Bruno fire destroyed dozens of homes, the city grew by 1.9 percent to 42,451.

One change surprised demographers: How California's prison realignment affected population. The state prison population declined late last year by 14,535 to 138,956 inmates as county jails accommodated more inmates.

That led unincorporated Marin County, home to San Quentin State Prison, to drop in population by nearly 800 people.

Contact reporter Matt O'Brien at 510-293-2465.