Does a kinyan derabbanan create a status of ownership on a d'oraysa level? This question is debated by the classical Achronim and comes into play on sukkos where the first day requires ownership of lulav and esrog to fulfill the requirement of "lachem". (We once discussed a proof of the Ketzos to resolve this question.)
Perhaps this question is at the heart of the machlokes Rambam and Ran regarding the gemara's warning (Sukkah 46) not to give a lulav and esrog to a child on the first day of sukkos before fulfilling one's own mitzvah. The gemara explains that a child can be koneh the 4 minim, but cannot be makneh the items back. Ran writes that the gemara must be speaking only of a very young child, because the Chachamim made a takanah that slightly older children (p'eutos) can buy and sell things, otherwise sending a child to the grocery story to buy something would be impossible. The Rambam, however, does not draw any distinction.
Apparently the Ran understood that the takanah empowering children to buy and sell is sufficient to allow them to be makneh the lulav back so its owner fulfills "lachem" on a d'oraysa level. The Rambam, however, did not think a kinyan derabbanan has any validity on a d'oraysa level.
The problem with such an approach is that there seem to be many proofs that the Chachamim can through hefker beis din make takanos that have a chalos d'oraysa. A few sugyos in shas (e.g. Kesubos 3) refer to the ability of the Chachamim to annul a marriage by declaring the kesef kiddushin ownerless. Clearly the women effected by such a takanah is not merely no longer married on a derabbanan level!
R' Shlomo Eiger's suggests (Shu"t RAK"E 221) that Chazal may be able to effect removal of ownership on a d'oraysa level, but cannot effect a transfer of ownership to a new party.
The Telzers (both R' Shimon Shkop and R' Y. L. Bloch) reject this distinction. Hefker without the ability to transfer ownership is an incomplete hefker because it has no effect on anyone other than the original owner. (This question fits well with R' Shimon's rejection of the Ketzos' model of hefker that we discussed back here.) R' Yosef Leib concludes that even the Rambam accepts the idea that a takanah derabbanan can effect a chalos d'oraysa in monetary matters. Where the Rambam and Ran differ is regarding the scope of this rule. According to the Ran, once the cat is out of the bag and there exists a takanah to allow children to shop in a grocery store, the same takanah has a chalos d'oraysa with respect to lulav. The Rambam disagrees and argues that the chalos d'oraysa is limited in scope to the narrow context that motivated the takanah's original creation. (Very Telzerish sevara -- the "sibah" is the geder hadin.) In the case of kesef kiddushin, the marriage is annuled; in the case of minor's kinyanim, only with respect to shopping is there a chalos d'oraysa to the kinyan. However, consequences that are a byproduct of the original takanah, e.g. now the child who can go shopping can also return a lulav, are not included in the scope of the chalos d'oraysa.
R' Bloch and R' Shimon's point relates more globally to how dinim derabbanan function. As opposed to dinim d'oraysa that say something inherent and intrinsic about a person or an object, dinim derabbanan just serve a functional need, but do not change the legal status or nature of things. This is a powerful sevara that explains many other ideas.... maybe more another time.