Step 1: Understanding population density.
Population density is calculated as the number of people per square kilometer. A densely populated continent is one where a relatively small land area supports a very high population.
Step 2: Analysis of options.
- (A) Africa → Although Africa has a large population, its vast land area lowers its density.
- (B) Asia → Asia has the highest total population in the world, but due to its massive land area, the density is lower than Europe's.
- (C) Europe → Europe is relatively small in size but has a very large population, making it the most densely populated continent.
- (D) North America → Has a large land area and comparatively lower population density.
Step 3: Conclusion.
Thus, Europe is the most densely populated continent.
\[
\boxed{\text{Europe}}
\]