The best replacement for splashtop is logmein.

The best alternatives to splashtop are rated as following:
★★★★★  logmein
★★★★  teamviewer
★★★  splashtop 2
★★★  vnc
★★  airparrot
★★  jump desktop
★★  air display
★★  screens
★★  kainy
★  doceri
★  pocketcloud
★  iteleport
★  nvidia shield
★  parallels access
★  pocket cloud
★  rdp
  remote desktop
  air display 2
  teamviewer ipad
  go to my pc
  gotomypc
  jump
  crazy remote

Your alternative for splashtop is not listed? Suggest!
Speaking about splashtop, one probably shouldn't forget about nvidia shield.

Other search terms related to splashtop and their ratings are:
★★★★★ nvidia shield
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Google Trends

Scale is based on the average worldwide traffic of splashtop in all years. Click on graph for more.
splashtop
logmein
teamviewer