Question: Probably questions about tires are an everyday-question on this forum. 

I own a GT mountain bike. I was running some tires more for dirt/off-road, but where I moved to live now I have also been riding a lot on tarmac/asphalt/pavement. So I was looking for some tires that would give me:

* **a good speed on these flat roads** (gosh, I have strong legs and still cycle fast, but these actual tires kill me)
* **still a good grip on off-road dirt/gravel**.

I came across the CONTINENTAL Race King ShieldWall (this is the upper-intermediate version of Race Kings). 

They sound to have a good grip for off-road, but also appear to be fast on road (of course not as fast a road bike, I'm not looking for it anyways). 

Now, bearing in mind my needs stated above, a question came to my mind - and when I search I only see topics/posts/answers from few years ago:

1. Should I run 2.0" on both rear and front wheel?
2. Should I run 2.2" on both rear and front wheel?
3. Should I run 2.0" on front and 2.2 on rear?
4. Or should I run 2.2" on front and 2.0" on rear?

PS: I'm also open to any other suggestions on tires :)

Answer: 
Looks like a good tire for both uses. The speed king would be faster on road, but not as good off road. If your off road is tending towards non-technical and dry hardpack, consider speed king. Size down not matter - narrow for more road/hard pack, wider for more technical off road conditions. 

Consider something like speedking rear and raceking front. With more weight (70%) on the rear, the rolling resistance is relatively more important on there ear. The race king ont he front will provide more predictable traction for steering and control when off road. 

One thing to watch is sealed/paved roads, especially when wet. As you lean into a corner, you transition onto the nobbly shoulder and loose traction when you most need it. Something like the speed king can catch an unwary rider out. 

Ideally you have two bikes, second best is two sets of rims, one for off road and other for on road.
An on-road tyre is smooth and has no significant tread, whereas an off-road tyre has some combination of large and small lugs to suit specific surfaces.

There do exist tyre profiles that are smooth around the "equator" but develop lugs further out around the edges.

It really makes little difference in the width of your options - 2.0 inches to 2.2 inches is 10% different on width, and you won't notice any practical difference. There's a current trend toward wider, but that's 28mm which is about half of your 50-55 mm options.

Also, you're riding a squishy MTB on the road - no amount of fancy tyres will make it "fast" so consider adding a second bike to your collection, rather than compromising the off-roadness of your existing bike. That second bike could be a rigid MTB/commuter, or a dropbar road bike. 

Depending on the condition of your current tyres, just keep riding them till they're worn out. As the lugs wear down, you will approach that "smooth band" around the middle. If your current tyres are still decent,then store them for some future rides, though be aware its irritating to change tyres a lot, and potentially damaging for the rims and tyres.