Great news. I have read to disbud the following year.

OldDutch they'll grow fairly fast. You dig them each year, right? After the first year they should be up to blooming size, the year after that big bulbs!

If I have plenty I'll just replant the blooming size bulbs and toss all the small ones, if I want more of a particular variety I'll plant the big bulbs and then stick the smaller ones between or around the edges to grow on. As you know it just takes a few years of this before you have more than you know what to do with!

Thanks for the advise. Next up is sorting to size holding out the largest 30 or 40 and then two smaller sizes of about the same count. The next size down will get disbudded, and the smallest may not get planted at all. I am wondering whether planting depth makes any difference or maybe am I digging them too late, missing the stage before division... I got a pile of questions, I also got a pile of tulip bulbs to play with. :)

They say planting deep limits division, it's an oft repeated bit of advice but I've never noticed a difference. For tulips what I see is that a hot dry spring makes for smaller bulbs which go dormant early, letting them go to seed definitely gives smaller bulbs, and dry soil while they are growing and blooming also stresses the bulbs and causes them to split into clusters of small bulbs.

Digging earlier or later shouldn't make much difference in splitting. While the tulip is in bloom is when the bulbs for next year are forming.

I thought that any big tulip bulb would split into several baby bulbs after their flowering and subsequent forming of the new bulb/s. Maybe, maybe not. Interesting to do some trials.

To grow the baby bulbs on, I would think just replant them in Autumn in a beautiful soil, water as needed and then wait until all the foliage has completely dried up (don't withhold water deliberately to make this happen sooner) before removal of foliage. (If removing the foliage at all.) Or leave the bulbs in the soil, if that area will experience dryness in summer.

I'd be surprised if the young tulips produce buds in Spring, but maybe they would, and if they did and you wanted them to put everything into increasing their bulb size, then remove the flower buds as soon as you see them.

I don't see many tulip flowers ending up producing seed. If so, I'd be inclined to save the seed and sow it. In theory anyway. But I usually forget where I stored my lovingly collected seed. Somewhere I have different batches of Freesia seed, some Dutch Iris seed, all sorts of seeds. And I am sure I once collected the seed capsule of a Tulip.