I was wondering that we always see the diameter of milky way but no one talks about its width. Even on google it is not there. This means that if I go up instead of forward then I would be out of milky in an instant?
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It is there, if you know where to look: https://en.wikipedia.org/wiki/Thin_disk https://en.wikipedia.org/wiki/Thick_disk
It's important to note that these are not uniform structures. That is, they get more diffuse the higher above/below the plane bisecting the Milky Way you go, with no sharp edges telling you where they end. The 'scale height' given in those articles is the height above the plane at which the density of stars goes down by the (somewhat arbitrarily chosen) factor of roughly 3.
Then there's the galactic halo, surrounding the entire Galaxy, which is highly diffuse in terms of stellar population. The point being, the 'thickness' of a galaxy (much like its radius) can depend on what precisely do you mean by it. I.e., it's a convention.