If you google for "current pass regulator" I believe you get a better quality set of results than if you google for "current amplifying regulator".
In fact, if you do it now, you might find an answer to your question in the first couple of hits.
But let me assist...
We'll start with a circuit suggested by
@Audioguru
View attachment 38930
The problem with this circuit is that using a 78XXL it is hard to get your 2A output current whilst keeping the current through the regulator low enough.
If we want Q1 to start to turn on at 10mA, R1 needs to be about 33Ω. Because of Rsc, that current will rise to about 20mA as the current limit starts to kick in. So, we have 60mA of possible base current for Q1. This means it will need to have a current gain greater than 33. A transistor with an HFE of 40 to 50 should be fine.
A
NJW1302GOS-ND seems to fit the bill (as do many others)
Using this, assuming an HFE of 75 to 150 at 2A, the current through the regulator will be between about 35mA and 55mA.
Under these conditions, you might have as much as 5V across Q1, plus another 0.7V across Rsc, so for an output of 12V you will need an input of at least 18V, more if it has significant ripple.
At lower input voltages, the current through the regulator will increase for a given output current.
An alternative is to replace Q1 with a darlington. If you assume an HFE of 1000, you can keep the current through the regulator much lower (and more consistent), however R1 needs to be adjusted to drop 1.4V at 10mA (68Ω should be fine) and it will only rise to 15mA as the current limit starts to kick in. The current through the regulator at this point will be approximately 17mA.
Note that the transistor Q2 prevents the current through Q1 from exceeding 0.7/Rsc A. If you attempt to draw more, the current will rise until the regulator is also at its limit. 78XX series regulators are protected to some extent against overcurrent and will shut down if badly overheated. However this shouldn't be considered a method of providing fool-proof short circuit protection.