Bonjour Denys, Cosmos atrosanguineus has tubers like a Dahlia but these are much more fragile. They do not take a totally dry situation like let's say in a box or paper bag in winter and are best kept in dry compost in a big pot in a cold and dry but frost free storage. It is a good sign that white little rootlets appear all over the tubers as often comercially available tubers are already dead on purchase, yours are definetly alive. The "welded" part is where the shoots will arise so this should be planted upward but still about 3-5cm below ground. Take care not to separate any of the tubers from the point where they are attached to the central shoot area as a tuber without an "eye" will produce roots but not a shoot and will therefore eventually die. If the separated tubers you talk about would have a bud at their tip they will grow but unfortunately most of the detached tubers do not have that bud. If you are unsure which end is which in the detached ones I recommend planting them horizontally and cover entirely with compost about 2cm high How long will it take from now on to have frost free weather in your garden? I am asking this because if you start these kind of plants indoors too early they will need a lot of attention and care and tend to etiolate which makes them vulnerable to direct sun and wind when planted out in the garden after the risk of frost is over. The shoots of this Cosmos will not tolerate any frost. You could delay sprouting by putting the entire tuber into a plastic bag and put it into the vegetable drawer of you fridge, BUT DO NOT FREEZE IT. Take care that there is not too much condensation in the plastic bag (a little is beneficial) and do not add any water by all means and check for mildew from time to time. (my fridge contains all sorts of things like that except food....) I would start a Cosmos indoors in a pot about 4 weeks before the end of frost danger or plant it directly in the garden about 2 weeks before the last possible frost (this is for European mild winters, where the soil is frost free a long time before the last air frost) Never plant into frozen soil. Good luck! Uli