Could the conservatorship end today?

After many months of back and forth, the fate of the conservatorship that has overseen Britney Spears and her fortune since 2008 rests solely in the hands of a probate judge in Los Angeles Superior Court, where a hearing that was set to begin at 4:30 p.m. Eastern may mark the end — or at least the beginning of the end — in a 13-year saga.

The New York Times has reporters at the hearing, but with no communications allowed from inside the courtroom, it will take some time to learn what was discussed and decided.

Both Ms. Spears, and, in a complete turnaround, her father, James P. Spears — who has long been the official steward of the legal arrangement — have said they want the conservatorship terminated.

“The time has come for Ms. Spears’s freedom,” the singer’s lawyer, Mathew S. Rosengart, wrote in a court filing late last month. Lawyers for Mr. Spears, who is known as Jamie, put it this way in their own status report this month: “Jamie believes that the Conservatorship should end, immediately.” Jodi Montgomery, the singer’s personal conservator, has also consented, according to court filings, and has worked with Mr. Rosengart on what he called a “termination plan.”

But it’s not quite as simple as the apparent consensus on both sides.

Typically in deciding whether to end a conservatorship, a judge will consider whether the conservatee has regained “capacity” — a term that generally refers to benchmarks in a person’s functional and cognitive ability as well as their vulnerability to harm or coercion.

But Ms. Spears’s case has been considered extremely unusual because she continued to work extensively as a performing musician and global celebrity, bringing in millions of dollars, while simultaneously being considered unable to care for herself by the court.

Since June, the singer has been adamant that the arrangement end without her having to undergo additional mental evaluations, and there is no public record of Judge Brenda Penny, who is overseeing the case, having recently called for one.

In a since-deleted Instagram caption, Ms. Spears seemed to allude to the possibility that the judge would concur. “This week is gonna be very interesting for me,” she wrote, using emojis for emphasis. “I haven’t prayed for something more in my life.”