It depends completely on the the mini. Some grow very rapidly and make excellent borders. That would include all of those in the 'Lemon Lime' family.
'Lemon Frost' last July 23
'Kifukurin Ko Mame' (of which I have 4 borders, but the ones close to a neighbour's Linden tree don't do as well).
That leads me to a second point. You need to have the minis in a location they like. I've noticed that most of the hostas that are close to either my Linden or the neighbour's don't do as well as they might. I think it's a water issue in that the tree takes it all. I have some of my minis in troughs and I now keep them in small pots rather than disturbing the roots twice each year. I don't trust them to overwinter in the troughs; so I sink them into my veggie garden. Most are growing better now that I just move the pots.
Others that have grown quickly for me -
'Lakeside Zinger'
'Kinbotan'
