UCrew is basically right. The Sheriff is responsible for all law enforcement in the unincorporated county areas and when a city doesn't have its own police force, it can contract with the Sheriff for police services. The Sheriff is also responsible for the courts and jails. Some cities have their own jails but usually those are only for temporary housing before being sent to the county jail. Sometimes the Sheriff can also be the Coroner for the county.

As far as jurisdication goes, I don't know about other states but I would assume that it is like California in that peace officer powers are granted for statewide enforcement which means in a legal sense, there is no jurisdicational limits on law enforcement. It would be more of a political thing.

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