The American cockroach adult is large, as long as your finger.
They are NOT a common cockroach in Auckland, and are often in established suburbs with older sewer systems. To establish themselves in a dwelling they need two things, (i) a source of heat (ii) a source of food. They breed very quickly and they are a health risk.
The American cockroach can be a sign there is a fault with the sewer pipes, that is allowing them up from the sewers into a building.
Wrongly named they are actually from Africa, but found commonly in the state of Florida, hence the name.