growing nice big garlic heads

At the moment I have an abandoned garlic bed overrun by weeds and it is full of little garlic plants. If I transplant these will it form sizeable heads? I don't like tiny cloves, too cumbersome.
And usual wisdom is that big cloves gives big heads, true or not? It contradicts somewhat genetics since every clove has the same genes.

I think they have the potential to form sizable heads. Some varieties of garlic are more prone to grow many tiny cloves and some will grow a handful of large cloves, just depends on the kind. One technique to get large heads of garlic is to cut the scape off when it appears and let the garlic grow a few more weeks, until the lowest 3-5 leaves turn brown, but pull one at random periodically during this time, the heads will split open underground when going past maturity, and if that starts to happen then it's time to pull them all. That's what I've been doing at least.

Thanks James! What is 'the scape"?  But ohterwise it seems to be fine with the little garlic plants I have.

The scape is the flower. It grows out of the center of the garlic stalk, and will curl around forming a loop. When these show up, cut them and that way the garlic plant will send all it's energy into growing big heads of garlic, instead of all that energy going into making a flower. Here's a picture of what they look like. They're also delicious, and can be often be used in lieu of garlic cloves. My wife makes a pretty tasty scape soup.

A larger clove grows a larger head not because of the genetics, but because there is more stored energy. The plant uses that stored energy when first planted to grow a root system. So a larger clove will grow a larger root system in the fall, which makes for a larger plant, which produces more energy to create a larger head throughout the summer.

I'm not sure about transplanting them (I've never transplanted garlic), but I'd think it wouldn't be as good of as option as just weeding and adding some compost to the existing bed. I've always heard garlic likes established roots.

The seedlings or however you want to call them (the leftovers of the unkempt bed) are pretty crowded and there are bare patches too and the soil is crappy.  That's why I want to transplant, but of course the cloves are not big.

I've transplanted leeks with much success, and the onion plants I grow are about the size of a pencil when they go in the soil and do very well each year, so I I like to think your garlic will transplant just fine.

Couldn't you just leave them for multiple years, as you can with other bulbs?

I also hate tiny cloves. In my experience, hard neck garlic has larger cloves than soft neck. The middles cloves from soft neck tend to be small. I've been trying to figure out the best thing to do with them, often they end up in my stock pot, so I don't have to peel them.

you are right there is actually a recipe with unpeeled garlic 'poulet canaille' it's awsome, there are about  60 cloves or more in that.

If you have a patch of many small garlic plants it may already be from cloves put in there a few years ago, so you'll probably end up with a heap of really small cloves.
It's a bit like strawberry plants; they keep on multiplying, but the strawberries become smaller and smaller.

Garlic is a very easy crop, but for big heads you want to put single, big cloves in fairly rich ground in the autumn, spaced 6 inches apart or so. Keep them free of competition from weeds, which should be fairly easy to do in winter.
If the cloves you end up with are very small, I would get new seed garlic; it is like Kyle Neath said: small cloves give small heads, although over time you could breed them back to size.
Cutting back the scapes will only help a little bit, and not all garlic makes scapes. Softnecks do as a rule not make flowers. Hardnecks do, that's why they are hardnecks: there's a flower stem in there. Of the hardnecks not all varieties have an elegant curly stem.

What you could do with your small garlic plants is to eat some of them as greens; consider them as small leeks with a garlic flavour. This is not unusual; also with garlic expected to grow to normal size people will sometimes harvest some of it early just for the greens.

Edit: I see you're in Australia, so the seasons I mentioned would be the wrong way around for you. You should be within a couple of months of planting time.