The direct replacement for
auto_ptr (or the closest thing to one anyway) is
unique_ptr. As far as the "problem" goes, it's pretty simple:
auto_ptr transfers ownership when it's assigned.
unique_ptr also transfers ownership, but thanks to codification of move semantics and the magic of rvalue references, it can do so considerably more naturally. It also "fits" with the rest of the standard library considerably better (though, in fairness, some of that is thanks to the rest of the library changing to accommodate move semantics instead of always requiring copying).
The change in name is also (IMO) a welcome one --
auto_ptr doesn't really tell you much about what it attempts to automate, whereas
unique_ptr is a fairly reasonable (if terse) description of what's provided.