A man can't discard his young children, or starve them:
כתובות סה ב
דרש רבי עולא רבה ... אע"פ שאמרו אין אדם זן את בניו
ובנותיו כשהן קטנים אבל זן קטני קטנים עד כמה עד בן שש
Rabbi Ula Raba said... although they said the a man is not obligated to feed his young sons and daughters, he must feed his very young sons and daughters. How young? Until the age of six.
The condition of daughters from marriage is slightly better:
משנה כתובות ד יא
בנן נוקבן דיהוין ליכי מנאי, יהויין יתבן בביתי ומתזנן מנכסי עד דיתנסבן
Mishna ktuvot p4 11
[One of the marriage conditions written in the Ktuva is:]
Daughters that you will have from me, will sit at my home, and will fed from my property until they we be married.
That's only until their puberty.
Also, a man must teach his son a profession:
קידושין כט א
ת"ר והאב חייב בבנו ...וללמדו אומנות
Our Rabbies said: Father obligation to his son... and teach him a profession.
About "transferring rights for gain" part:
A man can marry his young daughter to other, or sell her for maid*, but I believe that the premise is that he is doing it for her own good (he can't support her, etc), doing it for gain is being *&^@%#.
*Which is, again, for marriage. The master or his son must take her, or she is freed.