police and law enforcement

(Answer is applicable to the USA only): A warrantless arrest is never served. A warrantless arrest is performed. Following the warrantless arrest, the arresting individual (typically) or authority is required (usually) to provide the courts with a warrantless arrest affidavit wherein the person making the arrest articulates the probable cause for the arrest, which then is submitted to a judge for review. The arrested person will already be in jail or otherwise in custody (and possibly even bonded out), before the signed warrantless arrest affidavit becomes available to the arrested person.

in your presence the person is actually committing, about to commit a felony

Incident to an arrest

true