Extra-territorial Jurisdiction ("ETJ")
Governmental entities have territorial boundaries, and normally, their jurisdiction ends where those boundary lines are drawn. However, there are ways for a governmental entity to extend the territorial aspect of their jurisdiction.
For example, adjacent cities may enter into an agreement with each other, to provide for law enforcement officials from city A to operate up to a half-mile inside the borders of city B, and law enforcement officials from city B to operate up to a half-mile inside the borders of city A. This is common in metroplex areas, or when the border is marked by a river or an interstate highway. The same can occur at the county level. Such agreement would give each city an extra half-mile strip of ETJ area along that shared border.