I'm no expert here, but if you fill the holes with gravel, you have created a soak away. I had to dig one to replace the drainage pipes that muppet features who previously owned my house decided to smash up and fill in.
Can't give you any exact dimensions etc, but the bigger you can dig it the better - mine runs under the depth of the plant roots, or did, I suspect they've reached down to it now as it's a very exposed site. It copes with the run off from 4 terrace roofs in the worst rain and took about 12 girly size bags of gravel to fill with about a foot of soil on top.
The rain water runs quickly into the soak away and then..... soaks away over time. Not sure if that's of any help.
Cheers