Conceptual models rely on structural information to describe relationships among UML classes; among these, the whole-part (WP) relationship plays a fundamental role. This paper explores and analyzes the WP semantics at large with a focus on its software engineering use. The WP relationship has often been treated as a first-class modeling construct in object-oriented analysis, a subject of keen interest and it is considered important for UML modeling. From the scientific and philosophical aspects, a theory of parts forming a whole is a complex issue, loaded with controversies that are widely discussed. This paper aims to offer a semantic assembly model that is useful to describe WP relationships in conceptual modeling. We contribute to the WP research by conducting an ontological analysis using UML samples that exemplify the WP construct. The method of investigation is based on a model called a thinging machine (TM) to explore the WP semantics through applying TM to numerous existing UML models. The TM model uses the so-called thimacs (things/machines) to form building blocks for describing the domain at a three levels of description: static, events, and behavioral models. This approach contrasts the UML method, which is infected by a multiplicity problem concerning the integrated view of structure and behavior and how to associate diagrams with one another. This investigation s results point to a promising contribution to the understanding of the notion of WP relationship in UML.