Caitie Quinn said:
Like, is it "detectives" who do this (since I've already been told it would be "vice") or are they officers or something else. What's the process after they say, You're under arrest. I've just found out that in somewhere like Boston, they wouldn't use ink to fingerprint any more, it's digital (bummer, and yes, I double checked) -- What happens when they walk you in? Are you put in a cell then or processed and what is processed. Etc.
It's really
very dependent on the jurisdiction, and, up to a point, the exact nature of the arrest.
Is the call girl arrested in a sting? Is a warrant served on her? Is a warrant issued but not served, and does she then surrender herself into custody? Does she have a prior criminal history? Does she reside in the same city/state as the arresting agency? Is she charged with prostitution, or something else? Is it a misdemeanor? A felony? Are there any incidental charges (resisting arrest, providing false information to an officer, obstruction of justice, possession of a controlled substance...)? All that affects how it'll go, up to a point.
Many agencies don't have officers with the rank of "detective", anymore. But some do. Whether detectives - assuming there are any - from vice - which might go by another name, in some departments - are involved in the arrest at all depends on the circumstances of the arrest, and the way it's handled. Like, in a lot of places, if the notional vice detectives in a city PD worked a case against a madam, and got an arrest warrant for her from a judge, the resulting warrant would then be served on her, at her home, by deputies of the local sheriff's department - who might then book her into the county jail, and not the city one. And what happens to her thereafter could be vastly different than if she'd been arrested by the city, and could depend on the time of day, and day of the week. In some jurisdictions, under the right circumstances, she could be booked and released within two hours. In different circumstances, it might take six or eight hours to post bail. In still others, she might spend forty-eight hours in jail - and/or twenty-four hours in detox, and/or seventy-two hours in a hospital, if someone somewhere decides she might be a danger to herself.
So... it's kind of complicated.
If you want accurate details for a specific jurisdiction, ask the department's PIO. That's kinda what they're there for.

But keep in mind that how that agency does things might have no resemblance to how things are done five miles away.