I have been trying for decades to find an English equivalent for D. de H., at least as this term is used in Peru. I have read the best dictionaries available but none is satisfactory. Next of kin is too vague. Affidavit of Heirship is not good for Peru. An affidavit is a sworn declaration. So it would sound something like the heirs declare under oath that they are the heirs. Not so. In Peru, at least, the Declaratoria de Herederos is a formal judgment by a Judge who after examining all the documents of the prospective heirs and after announcing in the the official newspapers and gazettes that NN is dead and anyone who feels he is entitled should appear before the judge, officially declares that xxxx, yyy, aaa, etc. are the heirs. This procedure may take months. I my case I inherited a house from my widowed mother, I was the only child and even so it took me about two years to get the Judge`s DECLARATORIA DE HEREDEROS, naming me as sole heir. So perhaps "Determination.... as above would be closer".