～てあるSomething is done, Has been done, Remaining state

てある and っぱなし both describe ongoing states, but differ in tone. てある suggests something was done intentionally for future benefit. For example, 窓が開けてある means 'The window has been opened (for a reason).'. In contrast, っぱなし often implies carelessness. For example, 窓を開けっぱなしにして家を出た means 'I (carelessly) left the house with the window open.'.

てある and まま(に) both describe continuing states, but differ in nuance. てある implies an action was done for a reason and that the result remains. For example, 窓が開けてある ('The window has been opened.') implies that it has been left open for a purpose. In contrast, まま(に) emphasizes that the state remains unchanged, without implying purpose, e.g. 窓を開けたまま家を出てしまった ('I left the house with the window open.').

Both てある and ておく express actions done for future purposes, but with key differences. てある focuses on the resulting state after the action is performed, e.g. 窓が開けてある ('The window has been opened.', when it remains open for some purpose). In contrast, ておく emphasizes the action itself, focusing on preparation, e.g. 窓を開けておいた ('I opened the window.', implying that it was for future benefit.). Note also the different particles used.