I believe to mitigate unlawful arrest is why Batman leaves the evidence alongside the perpetrator and leave before the authorities arrive, so Gordon can say it's the police who's making the arrest, and the evidence just happens to be there shrug.
Sometimes Batman also intimidates goons or right-hand men to confess, so they do the court job for him. The rest he left to Gordon, Dent, Dawes, or whoever the current good lawyers and judge available. That's pretty much what they do in Year One and Begins, and I'm sure they continue to do now.
By now Batman helping the police is common knowledge, they just need a good enough case in court to counter that defense, and after most of Gotham's corruption is cleaned a lot of officials are willing to help anyway.