Now I am for 4 months in south america and here is how I did it:
I have bought a British registered bike.
For the aduana (border ) I show the original papers of the bike and power of attorney (carta de poder). Until now, I have cross many times the aduana between Chile and Argentina and had no problem.
For the police, because I don’t know Spanish and I do not want to confuse them and I will show them the original papers but with my name at the owner. Until know, in 4 months, police didn’t stop me 
As a conclusion I have the following papers:
1. Original papers of the bike with the former owner on them
2. Power of attorney (carta de poder) – paper that gives me the right to use the bike
3. Sales contract – because I bought the bike
4. Original papers modified with my name
Papers 1,2 & 3 are made at notary and they are official.
For the aduana I show papers 1& 2
For the police (it wasn’t the case and only not to lose time explaining about carta de poder) I show paper 4.

Additional information: it seems that is easier to by a bike from a traveler than a South America registered one. I didn’t have any problem until now. What I have heard but is not verified by me is:
- If you buy a Argentinean registered bike you cannot go outside of Argentina 1 year
- If you buy a Peru registered bike you cannot enter to Bolivia because they are having some political conflicts or something like that.
What I know for sure is that buying a bike registered outside of South America (I am a Romanian riding a British bike) you will not have any problem.

Hope that the information is useful and I go to enjoy the landscape 