There are two ways in which components are shared with party leaders when they need a component.
If a party member requires a component and you get that component via harvesting, monster splitting, or item disassembling, then every party member who needs that component will make a clone of that component. Plus, you get that amount as well. Thus, if you disassemble an item to get 2 Jewel Steel, every party member who needs Jewel Steel will get 2 Jewel Steel (even if they only needed 1).
Monster drops do not clone. Party members queue up for the components that do drop. If a party member grabs it, you don't get it. This is why you have the option to seize components. Seizing isn't necessary for monster splits (see above) because it is cloned for everyone.
Apart from these two methods, party leaders can also get components in the following way.
Buy in TownEdit
Active party members accrue gold as they fight (viewable under Check Items). If they need a component and it can be bought in town, they will use their own gold to acquire it. The conditions for this to occur are not clear.
Since split or disassembled components are cloned, try to maximize the number of cloned components by making sure as many of your party members as possible are at the same point in their upgrade tree, i.e., as many as possible need Jewel Steel before you disassemble something for Jewel Steel.