Introduction:
A subsidiary company is a company that is controlled by another company, known as the parent company or holding company. The subsidiary is usually a separate legal entity but is ultimately controlled by the parent company. There are several circumstances in which a company can become a subsidiary to another company.

1. Acquisition:
One common circumstance for a company to become a subsidiary is through acquisition. This occurs when the parent company purchases a controlling interest, usually more than 50%, in the voting shares of another company. Through this acquisition, the parent company gains control over the subsidiary's operations and management.

2. Merger:
In a merger, two or more companies combine to form a new entity. In this scenario, a subsidiary may be created if one company becomes the parent company and the other becomes the subsidiary. The parent company typically has a controlling interest in the subsidiary and exercises control over its operations.

3. Joint Ventures:
A joint venture is a business arrangement where two or more companies agree to combine resources and expertise for a specific project or venture. In this case, one of the companies may become a subsidiary of the other to facilitate the joint venture. The parent company provides guidance and support to the subsidiary in achieving the objectives of the joint venture.

4. Strategic Investments:
A company may also become a subsidiary through strategic investments. If a company acquires a significant minority stake, usually between 20% and 50%, in another company, it may gain enough control to consider it a subsidiary. Although the parent company does not have a majority stake, it can still exercise significant influence over the subsidiary's operations and decision-making.

Holding Companies:
A holding company, also known as a parent company, is a company that owns a controlling interest in one or more other companies. It does not engage in day-to-day operations itself but instead holds the shares or assets of its subsidiaries. The main purpose of a holding company is to exercise control and influence over its subsidiaries.

Functions of Holding Companies:
- Control: Holding companies exercise control over their subsidiaries through ownership of voting shares.
- Financial Management: Holding companies often provide financial management and coordination services to their subsidiaries.
- Risk Diversification: Holding companies diversify their risk by owning shares in multiple subsidiaries operating in different industries or markets.
- Tax Planning: Holding companies can take advantage of tax benefits by structuring their subsidiaries in different jurisdictions with favorable tax regulations.
- Strategic Planning: Holding companies develop long-term strategies and provide guidance to their subsidiaries to achieve their overall objectives.

Conclusion:
A company can become a subsidiary through various circumstances such as acquisition, merger, joint ventures, or strategic investments. Holding companies, on the other hand, are parent companies that exercise control over their subsidiaries and provide various services to them. These structures allow companies to expand their operations, benefit from synergies, and achieve strategic objectives.