Planning to club the website (ex:www.aabbcc.com) to their parent (ex:www.aa.com) website. Once added, the url will look (www.aa.com/aabbcc). Homepage as well as inner pages have a good number of backlinks.
Confusion with 301 redirects:
1) Should home (www.aabbcc.com) page be redirected to the respective sub page of the parent (www.aa.com/aabbcc) website or to the home page of the parent (www.aa.com) website?
2) Inner pages of (www.aabbcc.com) should be redirected to (www.aa.com/aabbcc) or (www.aa.com/aabbcc/innerpage)?
each url on the existing site should be redirected to the equivalent url on the new domain's subdirectory. www.aabbcc.com should be redirected to www.aa.com/aabbcc and inner pages of www.aabbcc.com should be redirected to www.aa.com/aabbcc/innerpage.
Redirects work best if they are one-to-one: each old URL redirects to one new URL, and each new URL corresponds to exactly one old URL. That applies to both human visitors and SEO. (This is, ahem, not always the case.)
The old root page may or may not need special handling. But if the entire old domain is moving to a directory of the new domain, then you've got the page www.example.com/aaa/ just sitting there, and you've got to do something with it. Unlike the deeper pages it can't be an exact replica of the old page, because now it also has to link outward to (probably) www.example.com/bbb/ www.example.com/ccc/ www.example.com/ddd/ and (definitely) www.example.com/