None of the three is very similar, but the best answer is constitutional monarchy.
The basis of a Republic is the separation of powers between the executive, the legislative and the judiciary.
In the Republic, each of these powers has its independence of action. The executive is headed by a President of the Republic, democratically elected by the population and responsible for domestic issues and also for the international agenda. Legislative power, in turn, supervises executive power and creates laws. Judicial power judges according to constitutional principles.
The dictatorship, the monarchy and the totalitarianism generally concentrate the power in the hands of a single chief and in nothing they resemble the Republica.
The constitutional monarchy, in turn, has similarities with the Republic, since it also respects the division of powers. However, there is no figure of a strong executive power, as it happens in the republic through the President. On the contrary, in the parliamentary monarchy that governs is the prime minister chosen by the parliament. The sovereign has the power of head of state, but it is something traditional and symbolic.
A good example of a republican country is Brazil.
An example of parents of constitutional monarchy is England.
