The decent young man stepping up to sudden responsibilities is a story that appeals to me. 
Papakiki!  has had some really nice moments. Sora and Miu’s attempts to manage the three year old Hina  whilst dealing with their own grief has been particularly well realised, along with the call back to Yuuta’s own past. When the focus is on the characters, and the story, Papakiki! works quite well.
I’ve previously described Mai-HIME as a series with a story just strong enough to overcome my distaste at the near omnipresent fan service . So far Papakiki! is also just on the right side of the line, but I reserve the right to drop the thing like a radioactive potato  if it goes too far.
So, like Kanamemo, this post might end up being the only post on this series.
Watch this space.
 C.f Usagi Drop, which I adored.
 Papakik! is apparently the commonly accepted alternative name, it even appears in the opening credits.
 I bought the basic set of Fluxx recently, the Radioactive Potato is one of the Creeper cards that can keep you from winning (most of the time, this is Fluxx after all).