I noticed that my seedlings don’t grow while transplanted in a large pot. What should I do? Should I use smaller pot to transplant seedlings? Is there any guidelines for that? What factor does actually affect in this case? For example, I transplanted some seedlings of hollyhock in a large pot after they have 2-3 true leaves and a single seedling from them I transplanted in a small pot. I observed the seedling in the small pot is growing well where the other seedlings in larger pots are not, even only one of those are now alive. Other have died after getting yellow leaves.
Whilst it can differ between the types of plant you're growing, and you've not said what you are growing, there are some general rules to observe with plants you've grown from seed, usually in a tray or shallow flat of some sort. Once they get their first set of true leaves, it's time to prick them out into either small pots or plant cell trays to allow each one to grow on and develop a good root system, using potting soil; a plant is only as good as its root system allows, so developing good roots is critical. Once they've grown on again, they can either be transferred to a somewhat larger pot, or into garden soil, depending on what you're growing. Some seedlings may need to be repotted into slightly larger pots 3 times before being planted into their final situation, but again, it depends on the plant. Some advice about pricking out - it's a delicate process, carefully done in order not to damage the seedling or its root - make sure the seed tray or flat is very damp, then take a thin, firm stick (I actually use the end of a child's small paintbrush), insert the stick close to a seedling, ease up the soil gently around it and take out the seedling, holding it by the leaves between finger and thumb.
There are reasons for doing all this potting; if you put seedlings straight into a large pot, what tends to happen is each plant does not form a compact, good root system; instead, they often put out a couple of thin, long, wandering roots. It is also difficult to get the watering right - the seedlings need to be kept watered, but a large pot has a lot of unoccupied soil which remains too wet from watering. Wet soil can affect gas exchange and cause the soil to become 'sour' and therefore an unhealthy environment for plants, but conversely, reducing the watering risks the seedlings dying from insufficient water. There are many 'how to' videos available on line to watch demonstrating this process - search for 'pricking out and potting on seedlings'.