An Android application called "IMI" was my Japanese tool for many years. It is better than anything else that I sampled both on Android and OSX. The most important feature is that it remembers much more of its state when applications are switched. So, if I cannot quite remember the whole kanji I'm looking up, I can switch back and forth. Most other applications will reset the component or radical lookup if you go through a home screen (or even carousel). Also, it supports component lookup, like the web-based Jisho.org. Many other apps only look up by a radical, like you would do in The New Nelson. Finally, IMI permitted to look up by English too. And, of course, it was 100% contained in the device with no need for Internet.
IMI was often confused with "Imiwa", another popular app, which even used a similar logo, or at least a similar color scheme.
Unfortunately, the author of IMI decided to stop supporting it, so Google removed it from their store. I can find APKs floating around, but... And now I cracked the screen on my Nexus 7, creating a sizeable dead area. So, that's the end of the road for IMI. I am looking for suggestions for replacements.