1) Encyclopędia Britannica, 1985, vol. 2, pp. 718-719, "Caesaropapism":
Political system in which the head of the state is also the head of the church and supreme judge in religious matters. The term is most frequently associated with the late Roman, or Byzantine, Empire. Most modern historians recognize that the legal Byzantine texts speak of interdependence between the imperial and ecclesiastical structures rather than of a unilateral dependence of the latter; historians believe also that there was nothing in the Byzantine understanding of the Christian faith that would recognize the emperor as either doctrinally infallible or invested with priestly powers. Many historical instances of direct imperial pressure on the church ended in failure . . . John Chrysostom and most other authoritative Byzantine theologians denied imperial power over the church.
It was normal practice, however, for the Eastern Roman emperor to act as the protector of the uiniversal church and as the manager of its administrative affairs . . . Emperors presided over councils, and their will was decisive in the appointment of patriarchs and in determining the territorial limits of their jurisdiction . . .
Caesaropapism was more a reality in Russia, where the abuses of Ivan IV the Terrible went practically unopposed and where Peter the Great finally transformed the church into a department of the state (1721), although neither claimed to possess special doctrinal authority . . .
2) Oxford Dictionary of the Christian Church, ed. F.L. Cross & E.A. Livingstone, Oxford Univ. Press, 2nd ed., 1983, "Caesaropapism," p. 218:
The system whereby an absolute monarch has supreme control over the Church within his dominions and exercises it even in matters (e.g. doctrine) normally reserved to ecclesiastical authority. The term is most generally used of the authority exercised by the Byzantine emperors over the Eastern patriarchates, especially in the centuries immediately preceding the Schism of 1054.