How does axon guidance system precisely targets specific axons?
In a nutshell, I would say neurons do have "specific instructions."  However, it isn't so much "ignore netrin X amount then stop."  It's more like "express receptors 1, 30, 48, and 62" which as a unique combination gets the growth cone where its going and prevents it from forming an erroneous connection along the way.  I've provided more context below that might help this make more sense.

A number of factors come into play with proper axon pathfinding and guidance, but I think the two below are sufficient for this:


There are different receptors present or absent on the cell surface depending on what cell type it is, which allows different cell types to respond only to specific cues. However, most developing axons express multiple types of receptors, so they can respond to multiple guidance cues (or respond to a cocktail of different cues).
There are non-diffusible signals present along the path in which the axon is growing.  You can read about one type here: https://www.nature.com/articles/nn.2231.  The main point about non-diffusible cues is that they can either stabilize the growth cone (which might promote growth or initiate the formation of a synapse) or they can repel the growth cone.  Therefore, they play an important role in informing the growth cone what is and is not the proper target.


There are now two things from your question should bring it all together.  First, you state that the precise path comes from a "specific combination of AGMs."  Exactly! The key word here is "combination."  Because there are so many AGMs that can affect the growth cone in so many ways, the combination of receptors (and intracellular secondary messengers) expressed on the growth cone and how they work in concert is what's critical.  Second, you state that growth cones will "ignore" potential targets as they pass them by.  That might sort of be the case (i.e., if a growth cone doesn't have a receptor for something the target is expressing, it won't "grab onto" or respond much to its presence).  However, it may also be that these potential targets express some non-diffusible cue that repels the growth cone, and it doesn't recognize that spot as a its final destination.

This article can also help provide more insight on the nuances of axon guidance:  https://dev.biologists.org/content/145/10/dev151415.long