Further, should the enemy lose their home base, they won't gain any points until its recaptured, regardless of how many other objectives they control.
If isolated, they contribute nothing to their team until reconnected. The goal of Supremacy is to completely drain the enemy of points earned from captured objectives, oftentimes done by cutting off said objectives. A feature specific to Supremacy is that objectives only produce points for the team that controls them, and only if they are connected to that team's home base.