New York Consolidated Laws, Partnership Law - PTR § 121-704. Right of assignee to become limited partner

(a) An assignee of a partnership interest, including an assignee of a general partner, may become a limited partner if (i) the assignor gives the assignee that right in accordance with authority granted in the partnership agreement, or (ii) all partners consent in writing, or (iii) to the extent that the partnership agreement so provides.

(b) An assignee who has become a limited partner has, to the extent assigned, the rights and powers, and is subject to the restrictions and liabilities, of a limited partner under the partnership agreement and this article.  Notwithstanding the foregoing, unless otherwise provided in the partnership agreement, an assignee who becomes a limited partner is liable for the obligations of his assignor to make contributions as provided in section 121-502 of this article, but shall not be liable for the obligations of his assignor under sections 121-603 and 121-607 of this article.  However, the assignee is not obligated for liabilities, including the obligations of his assignor to make contributions as provided in section 121-502 of this article, unknown to the assignee at the time he becomes a limited partner.