What's the maximum altitude ATC would deal with?
Any example of jets service ceiling certified for above 45.000? Commercial & Business jets?
There are many examples of aircraft with high service ceilings. While most commercial aircraft have service ceilings of FL410 and rarely fly even that high, many business jets have a service ceiling of FL510, such as the Dassault Falcon 7X, Gulfstream G650, and Bombardier Global Express.
That being said, military jets can fly higher and will be talking to ATC while in their airspace. Fighter jets are capable of high altitude flight, and planes like the U-2 and Global Hawk still fly up there as well.
In the US, all aircraft from FL180 to FL600 must be in contact with ATC, but above this they are not required to. ATC will still provide services when able though.
There is no maximum altitude for ATC service. ATC will deal with anything that flies over their airspace.
In the US, Class A airspace ends at FL600. Meaning if you fly above 60,000 feet (pressure altitude), you are not required to contact ATC, because it is Class E airspace. But that does not mean ATC will deny talking to aircraft at that altitude.
Practically speaking, very few aircraft (if any) can get above FL600. Chances are if you can get there, you are in an experimental military aircraft or spaceship.
Flights above FL400 are common for private and business jets. They are managed by ATC.
The other answer are correct that above FL600 you no longer need to be in contact however its worth noting there is some interesting historical implications to this.
The only civilian aircraft that routinely operated above the majority of other aircraft was the Concorde, which during its time cruised up around FL500. In his interview on Omega Tau one of Concorde pilots discusses this very situation. Essentially above ~FL450 they were allowed to transition altitudes as they saw fit and without contacting ATC essentially since they knew no one else was up there. He mainly discusses it in the context of fuel burn and how as the aircraft burned fuel it had a tendency to slowly drift up. ATC allowed them to do this (and not stick to an assigned altitude) as they could not really drift up into anyone.