Here are some examples of different personality disorders in terms of their tendency to seek relationships, versus avoiding them; and in terms of their tendency to dominate, versus submit to others:
In the dominant-affiliation quadrant is the Antisocial Personality Disorder. People with disorder are often described as quite charming and charismatic but their need for relationship belies a deeper need to dominate others for personal gain, via deception and exploitation. However, some people with Antisocial Personality use intimidation instead of charm and charisma to obtain their advantage. Their reckless disregard of others and lack of remorse and empathy often leads them to hurt other people.
Still on the dominant side, but with less need for relationship, are people with Narcissistic Personality Disorder. People with Narcissistic Personality Disorder are very preoccupied with themselves and their energies are often devoted to shoring up their own fragile sense of self-esteem. They have a strong desire to feel special and to be admired by others. Therefore, they often use others as a sort of prop to bolster their ego - other people are frequently seen as an audience who exist to satisfy their needs. When possible, people with this disorder will associate themselves with people who are famous, wealthy, or powerful. Their wish in assembling such a prestigious audience is that some prestige and glory will reflect back upon them; less important people who cannot reflect glory are not really worth their while.
In contrast, in the submissive-affiliation quadrant are people with Dependent Personality Disorder. They strongly desire to be in relationship with others because they feel they need to be taken care of, and have a hard time making decisions on their own. Since they are extremely afraid of being alone and worry about being left alone to care for themselves, they tend to avoid conflict. They don't dare to disagree with others or stand up for themselves. They fear that by doing so, they might lose the love and support they so desperately need. This tendency to avoid conflict at all cost places them on the submissive side of the power continuum.
In the submissive-detached quadrant are people with Avoidant Personality Disorder. Persons with this disorder are characterized by intense feelings of inadequacy and a fear of being shamed or ridiculed in social situations. Thus, they have a tendency to avoid social situations. Unlike persons with a Dependent Personality Disorder who have a strong need for relationship, these folks have neither a need for power, nor relationship.