Can't back-up new iMac with fusion HD. The back-up proceeds to within 10% of the total storage needed and then the "of" number increases. I suspect there is a problem with backing up the fusion drive. We have a new 3 TB time Capsule. Any ideas?

Hard to figure that growing backup issue.. it has hit a number of people.

Mavericks also is very buggy on the Time Machine side. Not at all impressed with the number of issues people are clearly having with it.

How much data do you have total?

So I have couple of bypass the issue suggestions..

1. Are you using ethernet? If not please do so.. you can even remove the TC from the network.. plug it by ethernet Lan port TC, straight into the computer and do the backup in full network isolation.

Over wireless there is too much back and forth for the first backup to run smoothly. If you do it this way actually turn wireless off in the computer.

Make sure ipv6 is set to link local as this is key to working in the new OS.

2. Do a TM backup to a USB drive plugged into the computer. You have USB3 on the latest iMac which is really very fast and it is a good trial to see if there is actually a more basic issue with the backup than the link to the TC.. USB drives of suitable size are cheap and usb3 is pretty well dominate now.. and hardly any more expensive than usb2.

When you setup the wireless and ethernet in the computer.. ipv6 will be on automatic.. this is wrong for the latest TC firmware and airport utility. http://support.apple.com/kb/TS4597

Go to the wireless and ethernet setup in preferences and change ipv6 to link local.

Once you do the big backup by ethernet the wireless will function fine for incremental.. it is obviously not estimating the size correctly..

A full back-up on the iMac would be about 650 GB. The partial updates that I have been trying start out at 115MB and keep growing indefinitely. The original back-up never finished nor have any of the follow-up attempts.

The first estimate should be the full backup but it will keep growing as the backup advances.. I would also delete any inprogress files to make sure it is not messing up .. delete even a sparsebundle if there is one for the imac on the TC and start afresh once you have ethernet connection.

See A10 here.

Pondini may have some other clues there to give you an idea of why the backup is slow or not finishing.. there is a lot of issues with TM when it decides not to work.