Working in Tunisian crochet makes a curling fabric because the bulk of the stitch remains on the back of the fabric for a lot of Tunisian stitches.
All the Tunisian designs I have done for Annie's and others, including the ones sold on my website, I have designed specifically to
alleviate this curling (unless the curling is a design element). Here are some tips to helping to alleviate the curling in projects in which you aren't using a pattern.
Try using a larger hook. With regular crochet, I usually use an I hook with Red Heart Super Saver, for example. But, if I want to use this same yarn with Tunisian crochet,
I will use at least a K afghan hook and have gone up to an L hook. You will be amazed at how well this helps with the curl. Also,
Tunisian looks best and works best when it is crocheted loosely! If you tend to crochet tightly, you may want to go even higher in hook size.
Another tried and true technique is to start off with a Tunisian Reverse Stitch or a Tunisian Purl Stitch for the first few rows. A Honeycomb Stitch Pattern or Seed Stitch Pattern will also work. (Please see my online videos.) Because Tunisian crochet can be so much like knitting, you can use the same tricks to combat the curl.
You could try blocking with a light spritz of water. Or, steaming. A thick border may help as well. Try the rope border for the Personalized Baby Afghan.
This is a nice thick border since you use two strands at once.
Lastly, be aware that the absolute worst stitch for the curling is the Tunisian Knit Stitch. So, you'll need to use even greater care in combatting the curling for that one. A Tunisian Extended Stitch is also helpful in combatting the curling, even when the predominant stitch pattern is Tunisian Knit.