We know relatively little about the processes by which an individual became emperor. We might imagine a  process of acclamation in which the emperor’s death was announced and the new emperor was immediately acclaimed. The Roman process was, however, complex.

The imperial position required the acceptance of power. The emperor needed people to follow his instructions. What mattered was that when the emperor instructed his servants, the senators, the generals, and the soldiers, they obeyed. This depended on informal power, the ‘authority’ of the imperial figure. Whereas Tiberius had legal authority at his accession, Gaius, Claudius, Nero, Otho, Vespasian, and Domitian could not rely on pre-existing imperium. Yet, it seems that they were able to exercise authority before any formal process of accession. This exercise of authority might include writing to the legions and their commanders, giving the watchword to the imperial guard, and receiving oaths of loyalty from various officials and magistrates.

The position of emperor was passed to the next generation through a process of hereditary accession, adoption, or through civil war. Nevertheless, the imperial position was technically a magistracy that had emerged from the Republican system; whatever the underlying politics, Romans needed to be appointed to a magistracy by legal act.

We have a single and fragmented copy of this legal act in reference to Vespasian:

Lex de imperio Vespasiani (Capitoline Museum): Image

The text (Latin and translation here) is not complete. The section we have makes repeated reference to the powers granted to Augustus, Tiberius, and Claudius, suggesting that it was these three emperors who were responsible for innovations in the imperial position.

The surviving clauses provide that

1. The emperor can make a treaty with whom he wishes: this gave him effective control over foreign relations.
2. The emperor can call a meeting of the senate and propose motions to the senate. 
3. Sessions of the senate called by the emperor will be able to pass measures as it would be if the senate meeting had been arranged by edict (presumably edict of the consuls according to normal procedures).
4. Persons who are seeking magisterial positions or other positions of power and who are recommended by the emperor are to be considered out of order (ie given special consideration) in every election.
5. The emperor has the authority to extend the sacred boundary of the city of Rome.
6. That ‘whatever he considers to be in accordance with the public advantage and the dignity of divine and human and public and private interests he shall have the right and the power to do and to execute’. This clause would appear to give the emperor unlimited authority.
7. That Vespasian is exempt from those laws from which Augustus, Tiberius, and Claudius were exempt.
8. Once this law is passed, whatever Vespasian decides should be done by edict shall be valid as if it were a decree passed by the people or by the plebs. 
9. (Sanctio) This clause would seem to suggest that legal action against the emperor’s acts is not allowed.

Clauses 6-9 would appear to govern the emperor’s relationship to law. The emperor is seemingly granted the power to make law (8). He has exemption from law (7; 9), though that exemption seems limited to specific laws. He also has unlimited executive power (6). These powers would seem so extensive that one wonders what other powers might be necessary for an emperor to rule.

Clause 6 might link to the powers of a dictator or the powers taken by the triumvirate. Taken together, the powers are enabling. They enable an emperor to act almost as he wishes, beyond constitutional check. It is thus a law which allows someone to rule unlimited by law.