Explanation:
In a partnership, there are different types of partners based on their level of involvement, liability, and rights. The options listed are all types of partners, except for option B, which is not a kind of partner.

Dormant Partner:
- A dormant partner is also known as a sleeping partner.
- This partner contributes capital to the business but does not participate in the day-to-day operations.
- They are not actively involved in the management of the business.
- However, they still have a share in the profits and losses of the partnership.
- The liability of a dormant partner is limited to the extent of their investment in the partnership.

Partners in Losses Only:
- Partners in losses only are those partners who have agreed to share only the losses of the business.
- They do not contribute to the capital or share in the profits of the partnership.
- Their liability is limited to the extent of the losses they have agreed to bear.
- These partners are uncommon, as most partnerships involve sharing both profits and losses.

Partner by Estoppel:
- A partner by estoppel is someone who is not actually a partner but is held out to be a partner by their actions or statements.
- This can happen when a person allows their name to be used in the partnership's business or represents themselves as a partner.
- Even though they may not have formally entered into a partnership agreement, they can be held liable as if they were a partner.
- This is done to protect innocent third parties who may have relied on the representation of the person as a partner.

Nominal Partner:
- A nominal partner is someone who lends their name to a partnership but does not contribute any capital or actively participate in the business.
- They are not entitled to a share in the profits or losses of the partnership.
- Their role is primarily to lend credibility or prestige to the partnership by allowing their name to be associated with it.
- A nominal partner's liability is limited to the extent of their name being used in the partnership.

Conclusion:
Out of the given options, partners in losses only is not a type of partner. Partners in losses only do not contribute capital or share in the profits of the partnership. Their liability is limited to the extent of the losses they have agreed to bear. However, in practice, it is rare for a partnership to have partners who share only the losses.

Introduction:
In the realm of partnership, there are various types of partners that play different roles and have distinct rights and responsibilities. However, one of the options provided in the question does not fall under the category of a partner.

Explanation:
Dormant Partner:
- A dormant partner, also known as a sleeping partner or a silent partner, is an individual who invests capital in a partnership but does not participate in its day-to-day operations.
- They are not actively involved in the management or decision-making processes of the partnership.
- However, they do share in the profits and losses of the partnership according to the agreed-upon terms.

Partners in Losses Only:
- This term refers to partners who are liable only for the losses incurred by the partnership.
- They do not contribute any capital to the partnership and do not share in the profits. Their liability is limited to covering losses only.

Partner by Estoppel:
- A partner by estoppel is not an actual partner, but rather someone who is held out to the public as a partner.
- This situation arises when a person represents themselves as a partner or allows others to believe that they are a partner, even though they are not.
- If a person is held out as a partner and others rely on this representation, that person may be considered a partner by estoppel and held liable for partnership obligations.

Nominal Partner:
- A nominal partner is an individual who lends their name to a partnership but does not have any actual interest or involvement in the partnership.
- They are not liable for the debts or obligations of the partnership and do not share in the profits or losses.
- The purpose of a nominal partner is often to lend credibility or prestige to the partnership.

Conclusion:
Among the options provided, the type of partner that does not fall under the category of a partner is "Partners in Losses Only" (option B). Partners in losses only do not contribute capital or share in the profits of the partnership; they are solely liable for covering any losses incurred by the partnership.