It should be significantly easier in space thanks to the lack of an atmosphere that would mess with your beam.

I tried to figure out just how accurately we are able to point stuff in space and found out the hubble telescope is able to "lock onto a target without deviating more than 7/1000th of an arcsecond, or about the width of a human hair seen at a distance of 1 mile." [1]

That's pretty amazing to me. Though I'm not sure if that would be enough, or whether we can be even more accurate.

With a laser beam it might also not be a problem if you're just slightly inaccurate, say only hitting your mark 70% of the time as long as you still manage to heat your target spot up sufficiently.

[1]: https://www.nasa.gov/mission_pages/hubble/story/index.html

I was more interested in the dispersion aspect of it. I'm not a specialist in this area, but I think a good dispersion rates for a high powered laser is in the area of 0.3 mrad regardless of the medium of transmission. And with that dispersion, targeting an object as far as Jupiter (600M km) would mean the beam would be 180,000km wide when it arrived.

Since people smarter than me have floated this as a way of deflecting asteroids, I assume there's some kind of way to focus it over those distances? It seems nontrivial though.