Strawberries... and a little helper

The main reason for posting today is that I have a question.

Strawberries are the one thing that I have managed to grow reasonably successfully in the past - unfortunately it was in a rented house (well, garden) so no sooner than I was able to bask in my triumph we had to move out. However, I did manage to stick around long enough to notice that the plant was shooting out it's tendrils and inserting them in to the soil at various other points in the garden; I presume this is it's own special way of ensuring the pitter-patter of tiny strawberry plants.

Now, here's my problem. My strawberry plant looks like this:

So what happens when the little tendrils are grown up and ready to flee the pot, and there's no where for them to go?

I have heard talk of a thing called a 'cutting' but I'm not quite sure if it's appropriate in this case. Any suggestions?

On a lighter note, I had a little helper in the garden today :)