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.
Arizona "association", "bank", "company", "corporation", "limited" or "incorporated" or an abbreviation of one of these words or the equivalent in a foreign language. Corporation may not use "bank", "deposit", "credit union", "trust" or "trust company" unless it also has a license to operate one. May not use "limited liability company" or "limited company" or the abbreviations "L.L.C.", "L.C.", "LLC", or "LC" § 10-401 Arizona Revised 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.