<p>The <i>k</i>-partite entanglement, which focus on at most how many particles in the global system are entangled but separable from other particles, is complementary to the <i>k</i>-entanglement that reflects how many split subsystems are entangled under partitions of the systems in characterizing multipartite entanglement. Very recently, the theory of the complete <i>k</i>-entanglement measure has been established in [Phys. Rev. A 110, 012405 (2024)]. Here we investigate whether we can define the complete measure of the <i>k</i>-partite entanglement. Consequently, with the same spirit as that of the complete <i>k</i>-entanglement measure, we present the axiomatic postulates that a complete <i>k</i>-partite entanglement measure should require. Furthermore, we present two classes of <i>k</i>-partite entanglement measures and show that one is complete while the other one is unified but not complete except for the case of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k=2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>