Concept: A valid adoption under the Hindu Adoption and Maintenance Act must satisfy statutory requirements regarding the person adopting, the person giving in adoption and the child to be adopted.
Step 1: Check the person taking adoption.
The person taking in adoption must have capacity and the legal right to take in adoption.
\[
A = \text{Correct}
\]
Step 2: Check the person giving adoption.
The person giving the child in adoption must have legal capacity to do so.
\[
B = \text{Correct}
\]
Step 3: Check the adopted child.
The child adopted must be legally capable of being taken in adoption.
\[
C = \text{Correct}
\]
Step 4: Check registration.
Registration is not mentioned as an essential requisite of valid adoption under this list of statutory essentials.
\[
D = \text{Incorrect}
\]
Therefore, the correct answer is A, B, C only.