What type of gov. Did they run?

The Hunnic ran a Monarchy government. He was the king.

Monarchy- a form of government in which sovereignty is actually or nominally embodied in a single individual (the monarch).[1] Forms of monarchy differ widely based on the level of legal autonomy the monarch holds in governance, the method of selection of the monarch, and any predetermined limits on the length of their tenure. When the monarch has no or few legal restraints in state and political matters, it is called an absolute monarchy and is a form of autocracy

http://en.wikipedia.org/wiki/Monarchy