When loaded, the ball is heavily marked by the cloth covering the lands and lightly marked by the cloth compressed in the bottom of the grooves.
To answer your question directly, the very surface at the muzzle is below groove depth, with the smoothed angle out to the tops of the lands perhaps using 1/8" to 3/16" maximum of the barrel's length. A patch and ball will sit on top of the crown, but leaning the rifle barrel over will cause it to roll off. It cannot be soved into the muzzle with your thumb.
The top barrel is a short section of barrel I purposely made a deeper crown on for load testing ITX hard-swaged balls. That is why it has a slightly different crown. It really loads lead balls and 10ounce denim easily. It has shallow rifling- no more than .005"- maybe .006" deep at the most and therefore is not suitable for heavy patches and bore sized balls. It's crown is a good 3/16" deep/long.
The largest muzzle is my 14 bore rifle's muzzle, which shows a crown of only about 1/8" deep with it's .012" rifling depth. At about the 11:00 o'clock position, you can see some rod wear in the corner of a groove next to the land. This was done with a tool-steel rod that I used to use for cleaning and loading ar the range. In thinking this over, it took maybe 5 years to do that and perhaps close to 3,000 shots and cleaning every 50 or so with that rod. It does not effect the accuracy that I can tell. I'm still able to put the first 5 into a 3" group at 200 yards off the bench. None of these barrels has rifling over .012" deep. Deeper rifling might extend the 'length' of the taper to 3/16", I'd guess, certainly not more.
As you can see, I do not use a file for crowning. I did read an article on Muzzle Blasts about a fellow who does, and the looked just great.