All right, I've gone all this time thinking "tank Poppy" was a joke of a build. She has no AOE and hardly any CC (a situational single target stun); her most notable attractions are a big damage Q and an ultimate that defends only herself and gives a big offensive boost to only herself. She has natural tankiness due to her passive, but her skills would seem to gravitate toward being a damage dealer rather than a damage soak, and she's certainly incapable of being a CC machine.
And yet, tank Poppy can be surprisingly effective, as I just learned.
I was top versus Darius, and he was competent, which in my experience means a lane where the goal is sheer survival, and it was a challenging goal at that. Partly that's due to a jungler who literally never ganked top.
(Our team: Poppy top, Nocturne jungle, Teemo mid, Ezreal/Taric bot. Their team: Darius top, Shyvana jungle, Kennen mid, Nidalee/dontremember bot.)
(Our jungler, a Nocturne, scared Darius a little at level 2, and showed up to wave hello once or twice later, but nothing I'd call a gank. He even ignored my request for him to cover top so I could recall, despite being at wolves and then blue; instead I died, came back to lane and THEN he shows up and takes some farm. Meanwhile he spent a lot of time going bot and instantly dying.)
So anyway, I'm barely managing to farm, and madly stacking GP5 and health items: Philo, Heart of Gold, Phage, Kindlegem. The only bright spot is that Darius had an awfully hard time finishing me off because I was turret hugging and a skilled Poppy (which I am) is extremely hard to turret dive. I escaped with sub-50 hp on at least two occasions (after Darius's ult and DOT finished ticking). Judicious use of Exhaust and my ult when he had a gank partner (unlike me) also helped.
Due to Nocturne's incompetence and enemy ganks, I eventually lost the outer top turret and around this time I realized that I was going to be building the tankiest Poppy I have ever built. Sure, I was working on Trinity, but I had Shurelya's (HP/regen), I was working on Randuin's (HP/armor/regen), and I was planning on Force of Nature (MR/regen). Combine this with the fact that although we had a Taric, he had been horribly feeding and in fact was much less able to fill the role of tank than I was (due to my solo-top levels of farm and my not being bad), and I realized what I had to do.
Perhaps you have noticed a trend here. Sure, I'm building HP to counter the true damage, and resists which are good against everyone, but what helps Poppy arguably the most is HEALTH REGEN. You see, her passive makes her harder to kill at low health, right? As she gets lower in health, non-true enemy damage is reduced by more and more, approaching 50%. So health regen becomes more and more effective at keeping her alive, approaching (but never reaching) DOUBLE normal effectiveness. This is why Poppy is so hard to finish off, and a tank Poppy with huge amounts of health regen can take this to ridiculous levels (although two or more enemies will still have an easy enough time, if they can corner her). Health potions are very powerful defensive items on Poppy for this reason in laning phase. They can be a useful buy on Poppy even after most champs would sell theirs as junk. (Life steal and spell vamp can also somewhat perform this function on aggressive Poppy builds.)
Anyway, back to the story. I was instrumental in the fight that turned this game around and gave my team real hope that they would emerge victorious. Both teams were playing footsie around Baron Nashor's lair. Enemy Jayce may or may not have been dead as a result of a surprise attack led by myself, but either way the enemy was fed and a strong threat.
I don't remember if I started the fight, but when the fight started, I immediately went for Kennen as his ult would really have been bad for our team. I wall stunned him into the Baron's gate and eventually killed him, and his ult didn't hurt my team. I was pretty low health but I still managed to wall stun Nidalee, allowing my team to kill her. Shyvana decided to try to finish me off, but I ran towards the blue buff golems; when she followed, I doubled back and wall stunned her, possibly killing her but certainly she died and I lived. By the time the fight had wound down, we had only lost one man and they only had one survivor. The other three took Baron while I recalled.
As you probably have gathered, tank Poppy is still a threat that must be reckoned with in her own right as a combatant; no champion can afford to just ignore her damage output unless they are also a tank or offtank at the very least. But unlike my normal Poppy build, tank Poppy doesn't just instantly die when her ult goes down. It takes a concerted effort from at least three enemies to burst her down in a brief period, during which time an intelligent team will be taking them apart. (That happened in another battle while we had Baron buff.) Now, one weakness of tank Poppy is the risk that a sufficiently coordinated and determined team will ignore her in favor of going after other targets while Poppy is ulting. Therefore, tank Poppy must make sure that she is as disruptive as possible to the enemy team's teamwork even if they try to work around her. Fortunately, I don't think this particular enemy team responded to me very well; I got the impression that my initiations either made them want to focus me or otherwise discombobulated them, as is the goal of any initiating tank.
After taking their mid inhibitor, we suffered a setback of almost getting aced and losing our mid inhibitor turret; but we regrouped and took Baron a second time, then downed mid inhibitor again, lured them into a battle over the top inhibitor turret, aced them, and won.
My health regen per 5 seconds (counting Force of Nature's special passive) was, I believe, 161.5, or over 32 health per second.