what brings about the capture of the escaped convict??

Compeyson is the convict with whom Magwitch had fought at the very beginning of the novel. After Magwitch reappears in Pip's life, Compeyson tracks him down and leads the police to him. There is a big scene in the water where the steamer hits Pip's little boat and everyone ends up in the water, Compeyson fights with Magwitch and presumably drowns, and the police end up pulling Magwitch from the water and arresting him.