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half-third-cousin 

1- Half-great-grandpibling's great-grandchild.
2- Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents and one great-great-grandparent in common.

double-third-cousin

Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents and four great-great-grandparents in common.

triple-third-cousin 

Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents and six great-great-grandparents in common.

quadruple-third-cousin 

Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents and eight great-great-grandparents in common.
Quadruple-third-cousin.

quintuple-third-cousin 

Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents and ten great-great-grandparents in common.

septuple-third-cousin 

Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents and fourteen great-great-grandparents in common.