Molluscum Contagiosum is the most likely diagnosis given the history (playmate having similar condition) and physical presentation, particularly the central umbilication and core of the papules.

Molluscum Contagiosum is a viral disease caused by a DNA poxvirus and transmitted via direct skin to skin contact or sharing objects touching the skin. Patients present with flesh-colored papules that contain viral bodies, usually appearing on the extremities, trunk and face. Highest incidence is in children less than 5 years of age. Usually, Molluscum Contagiosum is diagnosed by simple identification of the characteristic central umbilication and core of the papules. Treatment options include topical vesicants and cryotherapy among others. Or, simply waiting for disappearance is advised, as most cases resolve within weeks to months.

Atopic dermatitis, or eczema, is the most common inflammatory skin condition in childhood. It typically presents in skin creases or flexure surfaces as a red, pruritic dermatitis in variable stages of vesicles, scaling and excoriations.

Warts, caused by Human Papilloma Virus, are present in 10-20% of school-aged children. There are many different types, most appearing on the hands and feet.

Granuloma annulare, a benign inflammatory dermatosis, usually presents with groups of papules in an annular arrangement.

The morphology and history (that is, the fact that the mass was present fully-formed at birth) indicate that this is a congenital hemangioma. Infantile hemangioma are not present at birth, but rather proliferate during the first year of life. "Stork-bite" macules are not raised. Cherry angioma are typically found in older individuals and are much smaller.

EDIT - idiopathic