Most tyrant ants would appear to be single queen, single nest colonies. However, with meat ants known to also multiple queens in a colony, it is possible than some tyrant ants are also polygynous (multiple queens).
Tryant ants have an alate flight, where winged reproductive mate before founding a new nest. With meat ants known to also exhibit budding behaviour (where a new queen can leave the main nest with a group of workers and brood), it is possible that some tyrant ants also start new nests through budding.