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.
With the proper planning, limited liability companies can exist for generations. S-Corps continue to exist even if the owners or majority shareholders leave or pass away. C-Corps continue to exist even if the owners or majority shareholders leave or pass away. Non-Profit organizations and institutions survive after their directors leave. Sole Proprietorships do not exist when the owner quits or passes away.
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.