How to stop samsung galaxy s4 downlading messages from itunes/iphone

I transferred my contacts over from iphone to galaxy s4 using smart switch programme. For 24 hrs now it keeps downloading text messages too and no matter how many time I delete the threads from the messages they just keep re-downloading! It's driving me insane any ideas on how to stop this please?
Thank you

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Smart Switch program?

I suppose you're referring to the PC software, and not the Smart Switch app that you find on the Google Play Store which allows you to find matching apps?

If so, then you've probably selected the option of transferring text messages, after you've created your back-up from your iPhone.

I'm not fully aware of what options you've selected, but starting with the beginning, if you don't wish to transfer text messages then these are the steps that you should have followed (unless you did this exact same thing already):

1. Backup your iPhone to your computer (not to iCloud) using iTunes. Also the encryption option needs to be disabled
2. After the backup is created on your PC, close iTunes and connect your Samsung Galaxy S4 to your PC
3. Open Smart Switch and let it detect your device. After this step is done, the wizard will reach "Step 1", allowing you to select your iPhone backup
4. In "Step 2" deselect (uncheck) the type of data that you do not want to transfer to your Samsung Galaxy S4. (such as text messages)

I'm not sure if your SGS4 is now downloading while hooked up to your PC, or it does so remotely (if remotely then I'm not sure what's happening. Probably you've selected iCloud? I can't say...). Try to fiddle with the options again, and see if you can start over fresh.

I hope this helped!