Answer: (iii) arbitrary

In nearest-neighbour (k-NN) classification, a new object is assigned to the class most common among its $k$ closest labelled training objects. The decision boundaries it produces are exactly the perimeters of Voronoi diagrams: each training object owns a "cell" of the feature space containing all points closer to it than to any other object, and cell boundaries (perpendicular bisectors) form the class boundaries.

• These boundaries are not restricted to axis-parallel rectilinear lines (option i),
• nor to fixed oblique/hyperplanar shapes such as SVM or logistic-regression bounds (option ii).

For that reason the textbook (Han & Kamber) states that the decision boundaries of nearest-neighbour classifiers are arbitrary — they can take any irregular, data-driven shape determined purely by where the local training points lie.

Hence the correct answer is (iii) arbitrary.