What are the procedural steps the police are required to take once one begins to incriminate oneself in an investigation?
Police are under no obligation to stop one from incriminating ones self as long as one is aware of one's right to remain silent. For that reason, police routinely inform a person of his rights as soon as the person's liberty is restricted. Spontaneous or excited utterances are not excluded simply because the police did not have time or opportunity to warn one. After Miranda warnings have been issued, anything--literally--that one says can be introduced as evidence of guilt. Also, police are not obligated to give Miranda warnings until one is held in custody--that is one may not leave of one's own volition. If the conversation with police is merely routine questions, name, etc. and one blurts out incriminating evidence, then the police should advise one of one's rights under Miranda but don't have to tell him to be quiet.