Introduction:
The relationship between two words can be determined based on their meaning, usage, or association. In this case, we are given the relationship between "dwell" and "denizen" and asked to find a word that has a similar relationship with "inherit." Let's analyze the given relationship and apply it to the answer options to find the correct choice.

Understanding the Relationship between "Dwell" and "Denizen":
- "Dwell" means to live or reside in a particular place.
- "Denizen" refers to an inhabitant or resident of a specific place.

Explanation of the Relationship:
The relationship between "dwell" and "denizen" is that "denizen" is a noun that describes a person who dwells or lives in a specific place. In other words, a denizen is someone who dwells in a particular location. This relationship can be understood as follows:

- "Dwell" is a verb that describes the action of living or residing in a place.
- "Denizen" is a noun that describes a person who performs the action of dwelling.

Applying the Relationship to "Inherit":
Now that we understand the relationship between "dwell" and "denizen," let's apply it to the word "inherit" and the given answer options.

- "Inherit" means to receive money, property, or a title from someone who has died.
- We are looking for a word that has a similar relationship as "denizen" has with "dwell" when applied to "inherit."

Analysis of the Answer Options:
a) Acquire: Acquire means to obtain or gain possession of something.
- Acquire does not have a similar relationship to "inherit" as "denizen" has with "dwell." Acquiring something does not necessarily imply receiving it through inheritance.

b) Successor: A successor is a person who follows or takes over a position or role from someone else.
- While a successor can inherit a position or role, the relationship is not the same as "denizen" and "dwell." "Denizen" refers to a resident of a place, whereas a successor refers to someone who takes over a position.

c) Outcast: An outcast refers to a person who has been rejected or expelled from a group or society.
- There is no clear relationship between "outcast" and "inherit." Being an outcast does not imply receiving something through inheritance.

d) Heir: An heir is a person who is legally entitled to inherit the property, title, or position of someone who has died.
- The relationship between "inherit" and "heir" is similar to the relationship between "dwell" and "denizen." Just as a denizen is someone who dwells in a place, an heir is someone who inherits something.

Conclusion:
Based on the analysis above, the correct answer is option "D" - Heir. The relationship between "dwell" and "denizen" is the same as the relationship between "inherit" and "heir" because both pairs involve an action (dwell/inherit) and a person who performs the action (denizen/heir).