I just bought a used centurian anvil, it has some small feet welded on it, but I didn't think that would be a problem. After I removed the feet I realized that there were a couple hairline cracks near where the welds were. I think I can grind them out without removing too much metal from the anvil. I was thinking that if I just grind out the cracks I probably wouldn't  want to fill in the area with any welds as that seemed to be the problem in the first place. Thoughts? Thanks.

A picture would provide some information as to how to proceed. Welding something to a cast anvil would most likely end in cracks unless you heat the anvil and the feet and use appropriate rod. 

Take a pick or two of the anvil and the added feet and cracks 

HAZ cracking is the bane of welding the higher carbon alloys, especially in masses that will self quench.  The old anvils didn't have that issues as they had bases that were very low in carbon, then they moved into having higher carbon tops welded to cast low carbon steel basses. Whit the cost of the higher carbon alloys going down the completely higher carbon 1 piece cast anvils that do suffer from that issue.

First of all: if it's at the base of the anvil there is probably not a problem just leaving it alone---I have an old anvil with a foot broken off (sort of like a crack taken to the extreme...) I've never noticed any issues working on it for years.

If you have to weld it up proper preheat and slow cool will obviate any HAZ cracking issues. DON'T exceed the tempering temp of the face in preheat!

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