Del. Code Ann. tit. 13, § 951
The following persons, who desire to adopt any person or persons over 18 years of age, shall file a petition in the Family Court of the county in which any of the petitioner(s) or the person(s) to be adopted resides:
27 Del. Laws, c. 263, §§ 1-3; Code 1915, § 3067; Code 1935, § 3553; 13 Del. C. 1953, § 951; 57 Del. Laws, c. 402, § 2; 59 Del. Laws, c. 466, § 12; 62 Del. Laws, c. 402, § 1; 82 Del. Laws, c. 171, § 2