The antonyms for the phrase 'haddest connections with' can vary depending on the context in which it is used. However, some common antonyms can be distant, unaffiliated, estranged, unfamiliar, and disconnected. These terms suggest no association or relationship with the subject, which is the opposite of having a connection. These antonyms could be useful when talking about severing ties or ending relationships. On the other hand, if the intended meaning of the phrase is to have close or positive associations with someone or something, then the antonyms could be detached, isolated, alienated, or uninvolved. These terms illustrate a lack of intimacy or involvement with the subject.