(1) "Aid to dependent children or needy relative" means money payments with respect to or medical care in behalf of or any type of remedial care recognized under state law in behalf of a dependent child or dependent children, or a needy relative with whom any dependent child is living.

(2) "Dependent child" means a child under the age of eighteen years who has been deprived of parental support or care by reason of the death, continued absence from home or physical or mental incapacity of a parent and who is living with his father, mother, grandfather, grandmother, brother, sister, stepfather, stepmother, stepbrother, stepsister, uncle, aunt, first cousin, nephew or niece in a place of residence maintained by one or more of such relatives as his or their own home and who, if not granted aid, is likely to become a public charge or who would otherwise be deprived of proper support, care or training or a child under the age of twenty-one years who is attending high school or college or regularly attending a course of vocational or technical training. The term "dependent child" shall also include a child:

(a) who could meet the requirements of this section except for his removal from the home of a relative, specified in this section as a result of a judicial determination to the effect that continuation therein would be contrary to the welfare of the child;

(b) whose placement and care are the responsibility of the state agency; and

(c) who has been placed in a foster family home or child care institution as a result of such determination.

(3) The term "foster family home" or "child care institution" means a foster family home or child care institution for children which is licensed by the State.