Time Machine backup size

The initial backup will be the same size as on your boot drive with additional overhead for privileges and other under the hood reasons which I don't know.

Subsequent incremental backups will only backup those files that are new or changed with hard links for all of the other unchanged files.

An excellent source of Time Machine info is this tutorial site Apple OSX and Time Machine Tips.

It is recommended to have Time Machine external hard drive two times the size of storage of internal drive.

I really don't know all the "technical mumbo-jumbo" incremental and intial backup whatever. Maybe somebody else can explain.