I have always used loo rolls and/or very tall paper pots, unless I've run out and had to use 3"plastic pots. To stop them toppling, I pack them tightly into seed trays, as many as I can squeeze in, with a folded piece of newspaper between to differentiate types so that I only need to use one label for each type.
I plant them out deep, up to the first sideshoot, to make sure tops of pots buried. Peas of all kinds don't seem to mind this. I've had no probs with the pots rotting down, or collapsing too soon, although I have had strange fungi grow on the loo rolls occasionally (perhaps the glue used?). The fungi seemed to have no effect on the plants at all, I scraped them off and carried on. Last yr I was cutting into Nov. Got a good vaseful before I pulled them out, then. I can't sow direct due to mice eating the blinking lot!
Edd, many plants will do this. The bit where buds or sideshoots come out are called 'nodes', and they have a more concentrated amount of growth hormone in them, which is why we cut closely beneath one before inserting cuttings into a growth medium. They can produce shoots or roots, depending on the conditions. I have done it many times with interior plants when my ex-boss wouldn't pay for new ones! Although, I have to say I never thought of trying it with annuals. You know I have to try now, don't you?!
See, not only do you learn something new every day, you get new ideas to use what you already knew. What a great forum!