(CNN) Likely Democratic primary voters in California are about evenly split among the top three candidates -- Joe Biden, Bernie Sanders and Elizabeth Warren -- in the race for the Democratic nomination, while Texas Democrats tend to favor Biden, the nationwide frontrunner, according to new CNN polls conducted by SSRS in two of the largest early states to cast ballots next year.

In California, former vice president Biden (21%), Vermont Sen. Sanders (20%), and Massachusetts Sen. Warren (17%) are closely bunched at the top of the field with no other candidate reaching double digits. South Bend, Indiana, Mayor Pete Buttigieg holds 9%, followed by businessman Andrew Yang at 6% and former New York City Mayor Michael Bloomberg at 5%.

In Texas, Biden tops Sanders by 20 points, 35% to 15%, with Warren almost even with Sanders at 13%. Buttigieg follows at 9% and Bloomberg at 5%.

No other candidate in the field of 15 reaches 5% in either state. And in both states, about half of likely Democratic primary voters who have chosen a candidate say they have already made up their minds.

Breaking it down

The findings suggest a fierce fight for California's pool of more than 400 delegates.

In California, the state's diverse group of non-white voters is more closely split between Biden (26%) and Sanders (21%) than they are nationwide, partly due to Sanders' strength with Latino likely voters (Biden and Sanders are closer still among that group, 27% back the former vice president and 25% the Vermont senator). Warren slides behind Biden and Sanders among non-white voters (13% back her), but she is the only candidate to top 20% support among white likely voters (21% back her, Sanders has 19%, with Biden and Buttigieg at 16%). Yang stands at 8% among non-white voters in California, with Bloomberg at 5%, New Jersey Sen. Cory Booker at 4% and Hawaii Congresswoman Tulsi Gabbard at 3%. Buttigieg's support is almost non-existent among California's non-white voters; just 2% back him.

Biden holds a wide edge among the state's older likely Democratic voters (37% age 65 and up back him, ahead of his nearest competition by 23 points), while Sanders dominates among those under age 45 (32% in that group back him, a 14-point lead). Warren does better among college graduates (23% favor her vs. 11% among those without degrees), and women (20% back her vs. 12% among men).

Sanders' strength in California seems to rest on his policies. Across five top issues, Sanders leads the field as best able to handle health care and climate, and is about even with Biden, Warren or both on gun policy, the economy and immigration. And among those voters who say their priority is to nominate a candidate who can beat President Donald Trump, Sanders is well within striking distance of Biden: 23% in that group support Biden for the Democratic nomination, 17% Sanders, 16% Warren and 10% Buttigieg, suggesting electability is not as clear an edge for Biden in California as it has been elsewhere.

Sanders also prompts the strongest enthusiasm: 42% of likely Democratic primary voters say they would be extremely enthusiastic if he were the nominee, compared with 35% saying so for Biden, 34% for Warren and 23% for Buttigieg.

In Texas, however, it's a different picture, with Biden holding wide leads across nearly every major demographic divide among those likely to vote in the primary there. The former vice president also tops as best able to handle each of the five issues tested by no less than six points.

Biden prompts the highest enthusiasm among Texas' likely Democratic primary voters (44% say they would be extremely enthusiastic about a Biden nomination vs. 38% for Sanders, 31% for Warren and 23% for Buttigieg).

Trump backed by most Republican voters in California and Texas

On the Republican side of the primary picture, Donald Trump appears unlikely to face a serious challenge in either state. In Texas, 86% of likely Republican primary voters say they back the President, in California, it's 85%. Neither of his declared opponents reaches even 5% support in either state.

But Trump's approval rating overall is underwater in both states. In California, just 32% approve of the way the President is handling his job, while 61% disapprove. In Texas, 42% approve and 50% disapprove. Trump's numbers among independents (38% approve) and women (34% approve) in Texas would seem to suggest a warning sign for his general election prospects in a reliably GOP state.

But hypothetical general election matchups in the Texas poll point the other way.

Trump and Biden run about even in Texas among registered voters, 48% back Trump to 47% for Biden. Against three other Democrats, Trump holds significant leads: He holds 51% over Warren's 44%, and Buttigieg and Sanders each have 43% support to Trump's 50% in their matchups.

In California, however, all four Democrats tested against Trump lead the President by double-digit margins among registered voters, with little difference in support across candidates.

The CNN Polls in California and Texas were conducted by telephone among random samples of adults in each state. In California, results among the 1,203 adults have a margin of sampling error of plus or minus 3.4 percentage points; it is 5.2 points for results among the 508 likely Democratic primary voters. In Texas, results among 1,205 adults carry an error margin of 3.4 percentage points, while those among the 327 likely Democratic primary voters have an error margin of 6.6 points.

Correction: This story has been updated to reflect that the share of likely Democratic primary voters in California and Texas who have already made up their minds is among those who have already chosen a candidate.