As far as the children (A and B) are concerned:
a) A and B will be regarded as children born of unmarried parents
b) A and B will be regarded as children born of married parents
c) only Y will have full parental responsibilities and rights in respect of A and B unless
a court orders otherwise
d) both Y and Z will have full parental responsibilities and rights in respect of A and B
unless a court orders otherwise
c) only Y will have full parental responsibilities and rights in respect of A and B unless a court orders otherwise.
If A and B are children born of unmarried parents, they will be regarded as such. This means that they will not be considered as children born of married parents.
Regarding parental rights and responsibilities, option c) states that only Y will have full parental responsibilities and rights in respect of A and B unless a court orders otherwise. This means that unless a court decides otherwise, Y will have all the responsibilities and rights pertaining to being the parent of A and B.
Option d) states that both Y and Z will have full parental responsibilities and rights in respect of A and B unless a court orders otherwise. This means that unless a court decides otherwise, both Y and Z will share all the responsibilities and rights of being parents to A and B.