Under which circumstance would New York courts likely exercise general personal jurisdiction over a corporation?

General personal jurisdiction allows courts to hear cases against a defendant based on their strong affiliations with the state. In the case of a corporation, New York courts would likely exercise general personal jurisdiction if the corporation is "at home" in New York. This typically means that the corporation has substantial operations or significant business activity within the state, establishing a primary or dominant presence.

When a corporation is considered "at home," it usually refers to being incorporated in New York or having its principal place of business there. Jurisdictions look for a significant level of connection or integration into the state's economy and activities. If a corporation has substantial operations in New York, it indicates that its activities within the state are not merely incidental but are central to its business, warranting the state's jurisdiction over the corporation in a variety of legal matters, not just those related to its New York activities.

In contrast, maintaining a minor office or conducting minimal business does not typically meet the threshold for general personal jurisdiction, as these scenarios suggest a limited presence that might not justify the court's jurisdiction over broader claims. Hence, the emphasis on "substantial operations" captures the essence of what it means for a corporation to be truly "at home" in New York.