With the rapid expansion of artificial intelligence, elucidating the legal property status of algorithms and their governing property regimes has become essential. Algorithms are typically collaborative products, and the multi-layered structure of intelligent systems—encompassing source code, training data, models, and outputs—complicates establishing property status, defining the subject of right, and characterizing ownership. This study aims to determine the applicable ownership regime for AI algorithms—specifically, sole ownership versus co-ownership—based on the unity or multiplicity of the subject of right. Adopting an interdisciplinary legal-technical approach and a descriptive-analytical method, this paper argues that determining whether algorithmic ownership is individual or joint is a secondary inquiry, primarily dependent on establishing the unity or multiplicity of the subject of right. Three critical indicators determine this fundamental variable: (1) the governing protective regime (trade secrets, patents, copyright), defining the subject’s boundaries; (2) the technical structure (modular or integrated), indicating divisibility or indivisibility; and (3) the mode of participation in creation (distinct human contribution, intertwined collaboration, or autonomous AI generation), identifying right-holders and entitlement proportions. The findings reveal that establishing legal property status requires the algorithm to transcend abstract mathematical ideas, manifesting as a creative work or technical implementation with determinable boundaries. Consequently, where the subject of right is unitary, property rights emerge as joint ownership with equal or unequal shares. Conversely, sole ownership is realized only when multiple independent subjects of right are established. However, in autonomous algorithmic generation involving minimal human intervention, the absence of identifiable human contributors renders the conventional dichotomy between individual and co-ownership inapplicable, necessitating explicit legislative intervention to resolve this legal gap.