NEW YORK (Reuters) - Johnson & Johnson ( JNJ ) faces a critical test on Tuesday over its $10 billion proposal to end litigation alleging that its baby powder caused ovarian cancer, as it tries to convince a judge to sign off on its third attempt to resolve thousands of lawsuits through a subsidiary's bankruptcy.

U.S. Bankruptcy Judge Christopher Lopez in Houston will decide the fate of the company's latest Chapter 11 during a weeks-long court hearing weighing competing demands to approve the settlement or end the bankruptcy altogether.

J&J is attempting to use a subsidiary's bankruptcy to resolve lawsuits from more than 62,000 plaintiffs alleging its baby powder and other talc products were contaminated with asbestos and caused ovarian and other cancers, a claim that J&J denies.

Courts have rejected J&J's two previous efforts to resolve the talc litigation through a subsidiary's bankruptcy, but the company is trying again in a different bankruptcy court. It says the third effort can succeed where the others faltered because it now has votes showing a broad level of support for its settlement proposal.

The judge will listen to supporters and opponents of J&J's bankruptcy proposal in a marathon court hearing that will last until the end of February.

Lopez will consider evidence on a wide range of topics, including the validity of the votes that J&J gathered last year and whether such a wealthy company should be able to use a subsidiary's bankruptcy to protect itself from lawsuits.

J&J argues that bankruptcy offers a faster and fairer way to put money into the hands of cancer victims, who would otherwise face lengthy legal battles in a "lottery-like" court system that results in large verdicts for some plaintiffs and nothing for others.

Erik Haas, J&J's vice president for litigation, said in a statement that the bankruptcy proposal has "overwhelming support" from cancer victims and "affords claimants a far better recovery than they stand to recover at trial."

Opponents of the deal argue that the bankruptcy settlement should not bind those who do not like the terms and would prefer to take their chances in court.

By pushing the deal through a subsidiary's bankruptcy, J&J is trying to force women with ovarian cancer to accept lower settlement payments based on a deeply flawed vote, according to opponents.

The key witnesses in the hearing will include plaintiffs' lawyers who support and oppose the deal.

J&J has turned to bankruptcy to end the litigation, because U.S. bankruptcy law allows such a deal to bind claimants who would prefer to litigate their cases. A bankruptcy settlement would also prevent new talc lawsuits from being filed against J&J in the future.