A partnership is a business relationship entered into by a formal agreement between two or more persons or corporations carrying on a business in common. The capital for a partnership is provided by the partners who are liable for the total debts of the firms and who share the profits and losses of the business concern according to the terms of the partnership agreement.

Limited liability companies allow for a large variety of management structures based on your specific needs. Management structures for S-Corps are largely dictated by state and federal law. Management schemas for C-Corps are largely dictated by state and federal law. NPOs need to follow strict management laws to guard their non-profit status. Since Sole Proprietorships have only one member, there is no management structure.
Corp., Inc., Corporation, Incorporated: used to denote corporations (public or otherwise). These are the only terms universally accepted by all 51 corporation chartering jurisdictions in the United States. However, in some states other suffixes may be used to identify a corporation, such as Ltd., Co./Company, or the Italian term S.p.A. (in Connecticut; see under Italy). Some states that allow the use of "Company" prohibit the use of "and Company", "and Co.", "& Company" or "& Co.". In most states sole proprietorships and partnerships may register a fictitious "doing business as" name with the word "Company" in it. For a full list of allowed designations by state, see the table below.
Idaho "corporation", "incorporated", "company", "limited", or the abbreviation "corp.", "inc.", "co.", or "ltd.", or words or abbreviations of like import in another language; provided however, that if the word "company" or its abbreviation is used it shall not be immediately preceded by the word "and" or by an abbreviation of or symbol representing the word "and" ยง 30-1-401 Idaho Statutes
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.