Tristana is the closest thing to a split-pushing ADC that we have?
At least when I play Tristana, that's the strategy I use with her most of time: clear waves, splitpush. Her E makes taking towers extremely easy and fast.
Technically any ADC can splitpush, but on my opinion Tristana is far more suitable for splitpushing than any other ADC for a couple of reasons. She can clear waves pretty easily with Explosive Charge's passive, without even needing to use Statikk Shiv for that. She can evaporate towers by activating Explosive Charge on them and using Rapid Fire to take them faster. If anything goes wrong, such as enemies trying to stop me, I can just escape with Rocket Jump, and if needed, use Buster Shot to disengage from them.
By splitpushing and farming, I accumulate gold, and when late game comes, I have enough range and a powerful build to use at teamfights. While Tristana is less powerful than Jinx/Vayne/Kog/Maw/Twitch in terms of damage during late game, Tristana has an advantage over all of them: mobility (except in case of Vayne, which also has mobility; but Tristana has the range advantage over her)
People don't usually understand why I always does that, but this strategy almost always works.

is the closest thing to a split-pushing ADC we have. By epitomizing a split-pusher harder than anything else imaginable.