Kansas (except for banks) "association", "church", "college", "company", "corporation", "club", "foundation", "fund", "incorporated", "institute", "society", "union", "university", "syndicate" or "limited", or one of the abbreviations "co.", "corp.", "inc.", "ltd.", or words or abbreviations of like import in other languages if they are written in Roman characters or letters § 17-6002 Kansas Statutes
LLP, Limited Liability Partnership: a partnership where a partner's liability for the debts of the partnership is limited except in the case of liability for acts of professional negligence or malpractice. In some states, LLPs may only be formed for purposes of practicing a licensed profession, typically attorneys, accountants and architects. This is often the only form of limited partnership allowed for law firms (as opposed to general partnerships).

LP, Limited partnership: a partnership where at least one partner (the general partner, which may itself be an entity or an individual) has unlimited liability for the LP's debts and one or more partners (the limited partners) have limited liability (which means that they are not responsible for the LP's debts beyond the amount they agreed to invest). Limited partners generally do not participate in the management of the entity or its business.
Sole Proprietorship – A sole proprietorship, also known as a trader firm or proprietorship, is a business firm that is owned and run by one individual. A sole proprietor may use a trade name or business name other than his or her name. Registration not required – In summary, biggest advantage is quick formation and low compliance. However, the biggest disadvantage is unlimited liability.

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.