The quadtree itself doesnt do anything, its used as an aid to broad-phase collision detection to query the world to find sets of possibly colliding objects. The objects are usually represented by simplified geometry such as spheres or bounding boxes.
I would implement this by doing a breadth first kind of search down the quadtree to find pairs of potentially colliding objects (if two objects are in the same node, they are potentially colliding, even if one is in a subnode and the other in a higher level node)
You can either place the objects in the deepest cell in which they fit entirely, but that causes some objects that are located on the border of the high level cells to not really fit anywhere, possibly rising all the way to the root, such that the quadtree is only partially effective.
One solution to this is 'loose quadtrees' where the rectangles representing the nodes overlap (the node sizes have been essentially doubled along each axis). This means you can place the objects using their center position, and there will always be a node to place it in at a depth corresponding to the size of the object being placed. Naturally this means you also have to check adjacent quadtree nodes when finding sets of potentially colliding objects now that the nodes overlap with each other.
Im not exactly sure what you mean by depth, but if you mean the amount of levels in the quadtree or what levels the objects are placed in, that is probably very dependent on the situation. Its possible to make a quadtree that can create new levels as required to grow practically infinitely. If all your objects are of the same size, you can place them all to the leaf nodes of the quadtree (in this case a hashmap or something might work better, might not). If you have multiple sizes, you can use all depths.
You basically optimize it to the situation.
You should also consider the difference between 'dense' (???) and sparse quadtrees. Eg. Do you allocate nodes from somewhere as they are needed, or do you implement it using some multidimensional grids.