If you can get the surfaces clean and dry then you should use Bostick 1100
FS. It is usually only available from construction suppliers, not the home
stores. It sticks to concrete very well and it stays flexible permanently.
I forget the stretch ratio but I think it may be as much as 25% to 40%. So
a 1 inch crack could open to 1.25 or 1.40 inches and it would not tear. Tar
will get hard and then it won't stretch at all so if the concrete moves at
all it will open the crack again beside the tar. Be careful with the
Bostick as any messes must be cleaned up right away with acetone or they
will be permanent stains or lumps. It comes in normal size tubes so you
could do it yourself. It is quite thick so if you have a lot to do it is
hard on the wrists. I had a lot to do so I got a $20 power caulking gun
that runs on compressed air. Needed a lot of adjusting of the air pressure
so it wouldn't shoot out an entire tube in a few seconds.