Wow, why is everyone on the boards lately so damn fired up about every little thing? LH potential is anywhere from 20-27. HH is 28+ This means that he could improve 28, or he could improve 68 over the course of his career. A few attributes are more prone to having higher ceilings (PER, DEF, and LP come to mind) than some. From my knowledge, ceilings also depends on WE. A player with 10 WE will not reach his ceiling at all probably, whereas a player with 50+ will almost certainly max out.
Furthermore, the amount of STs you need before you can determine LH vs. HH vary. Sometimes you will get it on the first one you do, other times you might not get it, for the attribute you want, after 10-15 STs. There is no set amount.