The limited partnership agreement should address this. Also, if this split is amicable, you can agree to whatever additional terms you like. In many cases, a third party appraiser can come in, determine the value of the assets, and help determine the assets that each side walks away with. You will need to make arrangements for the obligations of the LP, and have a dissolution performed. These tend to be involved procedures, and each side should have its own counsel. Feel free to contact my firm if you wish to discuss this further.
You need to look to the governing documents of the limited partnership first. In most cases, the process "agreed to" by the parties will have been committed to paper. Second, you need to contact a lawyer to discuss other available options, and the consequences of each. The process of unwinding a partnership really cannot be summarized in short form here, and chances are you will have other issues to address and plan for, depending on your plans once free of the partnership.
I would agree with what has previously been stated by my collegues. In addition, I would suggest you look to see if a Buy Sell Agreement was signed. There are many factual issues which will determine which option is best for you (e.g., financing, who want to stay in the business vs. leave, non-competes, outstanding liabilities, lease assumption and personal guarantees, etc.) You need to speak with an attorney who specializes in business dissolutions to guide you through the process.
