The Roman emperors used to adopt the next chosen emperor and pass him the family name "Caesar", as did Julius Caesar, probably without trying to create a tradition, with Octavius.
No -- this was done by the 'Five Good Emperors' (Nerva, Trajan, Hadrian, Pious, Aurelius) and done more out of the lack of suitable male Heirs than of a notion to go outside the blood line. The Five Good Emperors ends to Aurelius, who -- coincidentally enough -- was the first to name his son as Heir. His son was Commodus, and was (by the account of contemporaneous, biased sources) a bad emperor -- although there is thought that many of his evils were embellished by detractor historians.
Otherwise, the title of Imperator/Augustus went to male blood heirs or usurping Generals (in one case, to a wealthy man who bought off the Praetorian Guard).
