Well, we have to assume that trolls have DNA, since it's safe to assume they share a common ancestry with humans and a variety of other fantasy creatures. And I think it's reasonable to assume that their regeneration functions in a similar manner to "ordinary" cell repair functions, with the exceptions that it occurs much more quickly (greatly enhanced metabolism on demand, perhaps? worth investigating), can repair catastrophic damage such as brain trauma or amputation, and is inhibited by strong acids and fire.
Given these axioms, it is reasonable to assume that trolls create new cells with their old cells' DNA as they replicate. As a result, new tissue would be recognized as foreign by old tissue, which could cause all sorts of problems with the immune system. It could be possible for trolls of similar blood type to undergo a blood transfusion or organ transplantation, but piling tissue from one troll onto another so that they "fuse" together is unlikely to work unless the trolls share DNA (identical twins, for instance).