The governing document of the LLC is called an operating agreement, and it is within this document that the members lay out all important provisions, such as standards for LLC governance, ownership parameters, and rules around member changes (adding or removing members, or what happens in case of death or incapacity of a member). The operating agreement is an internal document and is an agreement amongst the members or owners, which means it is not recorded with the state.
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.
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.