What exactly is the role of someone who mains solo top?

• Is it to just keep the other top busy and keep him out of the early fights?
• To push the tower as fast as possible?
• To gank middle lane?
• To shut down the other solo top?
• Or to simply just farm and hold the lane?

I myself solo top all the time, and I hardly lose to my opponent, but my team still ends up dropping the ball..
What should I do as a solo top player that will benefit my team the most?
What exactly is the role of someone who mains solo top?

To beat the enemy team.

Not helpful. Don't be a ****.

I think this is a good question, I play solo top a lot and I suspect the best answer may just be all of the above. A good solo top will either knock his tower down early, keep the opposing top shut down, gank mid, maybe even do a bit of counter-jungling. A the very least, you should be able to hold your lane and farm well and keep ahead of the curve, to make sure you are well geared for upcoming teamfights. This is especially important I think if you play a tank/initiator.

I'd say push tower if you're losing lane so you can go help your team. If you're winning shut your opponent down and try to get the jungler to come gank you multiple times.

it depends on what stage of the game you're talking about. a solo top in early game is to get farm in his lane while harassing his enemy and trying to zone them. mid game a solo top should have his tower gone and should be helping gank mid if a situation arises. late game the solo top is supposed to stick to the enemy AD carry and annoy the hell out of them during the team fight. These are my PERSONAL experiences and am in no way representative of any pro etc etc.

It's the only correct answer, because what the ideal action is 100% dependent on the situation.
There's too many factors to give a real answer to the question. What are the team comps? Who is your lane opponent? What's happening with buffs, dragon, and/or baron? How are your other lanes doing? Where is the enemy jungler? Where is your jungler?

The most general thing is that you always want to win your lane, but even that can have many meanings. And sometimes that just isn't possible, and what you really want to do is not LOSE your lane.

Edit: Actually, the most general things are:
1. Don't die
2. Get as much CS as possible.
3. Get as many kills as possible
4. Deny as much CS as possible
5. Prevent as much damage to your own tower as possible
6. Don't die
7. Work towards the end goal of getting their Nexus down (may involve killing some towers and going to other lanes at some point).

Which is applicable to all lanes and can easily be summarized by "beat the enemy". There is no one-size-fits-all strategy for laning.

I basically second what Admiral Love said. You should be doing several things at once. However, not every game is the same.

Foe's Advantage:
Let's say you picked top first and you get countered hard. Your #1 job is to survive the laning phase while protecting your turret. Let your jungler know when you need him.

Your Advantage:
Now let's say your opponent picked first and you picked a hard counter. You must outfarm and/or out kill your opponent. If you are able to score a kill or push to the turret help gank mid by all means. Don't be satisfied winning your lane if you can help your mid win their lane too.

Fair Fight:
If the fight is about even the goal is to end the laning phase in a better position to contibute to team fights than your opponent. Generally speaking this means outfarming and/or out killing your opponent. Limiting your time away from lane is key to staying equal or ahead in levels too (don't die and shop fast).

Of all the "roles" you identified I would say that "To push the tower as fast as possible" is the least important. Taking a turret in the early game is slow going and puts you at serious risk for getting ganked and killed. It is much safer starting mid-game. If you've done everything else right, that turret is coming down eventually. The biggest exception would be if you just had a successful jungle gank and you have a group of minions providing turret cover. At best, the opponent is going to have their jungler or mid come top to protect the turret, but you are in little danger.

Much better answer. Thanks for not being a ****.

Dont die, Farm.

Anything past that is really optional. If you have the opportunity to get kills, that's great. If you're left free long enough to gank mid then go for it (that being said... so often better to just free farm top if it's early or mid game)

Mid game and later, you need to show up for any skirmishes you can safely get to and definitely be present in team fights.

Keep wards up top lane and if possible in their jungle (having a ward on their red buff around mid game really helps shut down their jungler just by that bit of extra map awareness + opportunity to gank with your own jungler.

That being said... the only time I have a problem with top lane (keep in mind, I main mid) is when they die multiple times or do not farm. if they can just maintain an even (or close to even) score, I'm plenty happy. They should avoid getting ganked, keep ward up in river, be aware of if it's warded (to call for ganks from mid and jungler) and simply farm up so they can be of use late game.

I'm pretty new to the LoL forums but to answer this, I jungle a lot and my mostly second role is solo top, but anyways in my opinion I think is to get top farmed and possibly fed with the jungler actually doing things. Now we've had all of those solo que's where your solo top and some one jungles and you have like jax and sion top and they just say "I don't gank until level 6 or above" so in those scenarios what I do is just wait till they push the minions to the tower and last hit, if the enemy team has 2 solo top's then they wont get those farms or they'll be competing for it. now the second scenario that has happened to me is if there are 2 top and your solo, the other one will tend to jungle, in that case I just play aggressively and try to kill them 1. the reason why I specifically do that is if they die as soon as his lanning partner leaves to jungle they get angry which in my opinion clouds their game play so their just focused on raging on the other person. 2. if your still getting owned by the other one for either him out playing you or just out harassing you with is like I said before to just farm or let your jungler know that you need help, most solo tops are shy and when they die they start yelling at the jungler when its a bit late, so don't be shy to call your jungler solo top isnt just to get the solo top nice and farmed or fed its also a win for the jungler because of the ganks. And this is something you could consider "extra" is to kinda counter jungle but make sure its warded and same with your jungle so you can own them. I'm pretty sure I explained a more of a "how" than a "why" but this is all I could think of at this time.