UPDATE 2-Democratic debate highlights: Biden the favored target

(Adds exchanges on race)

By Amanda Becker and Jarrett Renshaw

DETROIT, July 31 (Reuters) - Democratic front-runner Joe Biden was again the main target of his rivals at the second presidential debate on Wednesday, as many of the nine other candidates on stage took aim at his track record on race, criminal justice, immigration and healthcare.

"Go easy on me, kid," the former vice president told Senator Kamala Harris of California with a smile as they greeted each other on stage before the debate began in Detroit.

But neither one had any plans to go easy, and they went after each other in a series of tough exchanges.

As the highest-profile candidates on the stage, both of them were also repeatedly targeted by the other candidates.

Biden did better than at the first round of debates in Miami last month, but his performance was still uneven. Harris was also on the defensive at times, failing to repeat her dominant performance in Miami.

Amid feisty exchanges, some candidates warned they should be focusing their fire on their real target: Republican President Donald Trump.

Here are some highlights from the debate.

MEDICARE FOR ALL

The first question went to Harris, who was asked to respond to the Biden campaign's characterization of her recently released healthcare plan as a "have-it-every-which-way approach."

"They are probably confused because they have never read it," Harris responded.

She said her plan is a response to listening to voters, who want public and private options for now, with 10-year phase-in period to transition to a Medicare-for-all system, as opposed to a four-year phase-in period offered by progressive U.S. Senator Bernie Sanders of Vermont, who took part in Tuesday night's debate.

Biden said Harris did not fully explain how she would pay for her plan. Harris countered that Biden's plan would leave 10 million people uninsured and called it the "status quo."

The question led to some of the most clearly articulated positions on expanding access to health insurance the candidates have offered to date.

Senator Kirsten Gillibrand of New York, another of the 10 candidates on stage, said Democrats need to remember that Republicans are chipping away at the Affordable Care Act enacted by former President Barack Obama and that Democratic candidates are at "risk of losing the forest for the trees."

"This pitting against progressives, against moderates, saying one is realistic and the other doesn't care enough - that to me is dividing or party and demoralizing us in the face of the real enemy here," Senator Cory Booker of New Jersey said.