Is there the current amplifier IC to contain:Iout>3A?

Answer 1

Apex makes high current output amplifiers. They are not current amplifiers, they are operational amplifiers, so you could modify their input circuit to sense current.

http://eportal.apexmicrotech.com/mainsite/products/Matrix_Linear.asp

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Answer 2

That's a little imprecise

Let's take an AUDIO IC you can get those easily with 3A outputs

but there's no such thing as a "current amplifier IC"

you get Volts in ...amplified volts out
at up to a specified current (or load)

Answer 3

Any transistor where the load is connected between emitter and 0 Volt is considered a "current amplifier".
If you need a high current amplification, then you would use what's called a Darlington Transistor. Since this consists of (usually) 2 transistors wired as emitter followers, you could call that an IC.
Motorola TIP140 .... TIP147 are 10 Amp types, for example.