Supply curve when the marginal cost is zero
Took me a bit, but I have figured its out:

The single firm's supply curve is defined as it marginal cost, as long as MC is above it average cost
A firm would not sell below its average cost, since it would loae money, Mathmatically we can define, for the single firm 
S = MAX(AC, MC)

Our basic assumption,for this discussion, is that MC = 0

Under the basic assumption and that costs are positive, obviously, then, the supply curve will always equal AC:
S = MAX(AC, 0), AC > 0
S = AC

The other conculsion from the basic assumption is that the production function, under the costs limit, is completely unaffected by quantity
Intuitively: its costs the same to produce 100 products and 1000 products. 

If the Total costs function, as a function of quantity, is fixed, then the average function is:
AC = TC/x

In that case, we'll get a supply curve, though a very special one:
It'll decrease price as a result of increasing quantity, and prices will aspire to zero. always

Update:
Allowing myself to add a link to an article I wrote on the topic:

Start-Up economics: the disrupt model