admit: To agree to the truth of, usu, something bad.

　　It suggests reluctance or possible objection.

　　He admitted his crime/stealing.

　　(自白 供认) confess: To admit guilt as to a crime or as to a shortcoming, in the sense of making known to others one's own error or wrong doing.

　　He confessed his fault/doing something wrong.

　　acknowledge: to agree the truth of, recognize the fact or existence of what have said or done, good or bad.

　　It emphasizes openly in a embarrassing or awkward and usually not voluntary way.

　　I acknowledged my signature/mistakes/errors/having been defeated.

　　grant: To admit or to agree something is true.

　　I granted his request/his honesty.

　　take sth/sb for granted.

　　concede: To admit as true, just or proper often unwillingly because of overwhelming evidence.

　　I conceded you that point, but I still think you are wrong.

　　recognize: To accept or acknowledge it.

　　It refers to something about law and diplomacy.

　　The new regime was recognized by China.