When two hijacked jetliners struck the World Trade Center towers in New York City on the morning of Sept. 11, 2001, Mayor Rudolph Giuliani became the face of a city struggling with tragedy, a ubiquitous presence projecting authority, assurance and control. The reputation he forged that day would be tarnished with time, but it became a model for mayors facing crises across the country.

As Mayor Karen Bass of Los Angeles confronts a city dealing with devastating fires, her performance has raised questions, even among her supporters, about whether she can become the dominant executive leading a city through a crisis that New Yorkers saw more than 23 years ago.

Some of those concerns reflect her relative lack of executive experience — she is a former member of Congress and the California assembly, where she served in the powerful role of speaker. And some of those concerns have to do with the fallout from her absence from the city when the fires broke out.

But the question of who is in charge — of who is playing the role in Los Angeles that Mr. Giuliani did in New York, to use one example — is also testimony to the diffusion and, at times, dysfunction that make up the core DNA of the governance of the greater Los Angeles area. That muddled authority is a sharp, and by design deliberate, contrast with New York, Philadelphia, Chicago and other cities that are dominated by powerful, high-profile mayors.

The city of Los Angeles, with a population of 3.8 million, is one of 88 different cities that make up the county of Los Angeles. That county, with a population of 9.6 million spread across 4,751 square miles stretching inland from the Pacific Ocean, is controlled by a five-person board of supervisors, each one representing 1.9 million people. Each of those supervisors rivals the mayor of Los Angeles in clout as they oversee their own fiefdoms in the nation’s most populous county, even if they are relatively unknown by constituents.

Within those vast borders, there is a Los Angeles Police Department and a Los Angeles County Sheriff’s Department, as well as an additional 45 police departments protecting, to name a few, Santa Monica, Long Beach, Inglewood and Pasadena. There are dozens of municipal fire departments, including one that serves the city and another that serves the county.

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