In TTL, Andreas would have inherited the archduchies of Austria and Further Austria upon the death of Mathias. Albert would have had the right to rule in his behalf as regent and most likely Mathias would have arranged for the Austrian Estates to recognize Albert as regent. I do not know what the age of majority was in Austria, but Emperor Albert II assumed power in Austria in 1411 when he was thirteen, so Andreas could use that as a precedent. Bohemia and Hungary are trickier due to the elective nature of their monarchies. Mathias could try to get Andreas elected king in both countries but I can not imagine the estates of either kingdom wanting to go through with a lengthy regency. In OTL, Ladislaus the Posthumous was elected to the thrones of both Bohemia and Hungary as a child in 1444 and had a different regent for each kingdom. Even if Mathias were able to select Albert as a regent for his son in both Bohemia and Hungary, upon Albert’s death the estates of both kingdoms would chose their own regent.
Mathias would also probably attempt to have Andreas elected king of the Romans. If Mathias were successful in his efforts and Andreas became emperor, then by virtue of the Golden Bull the imperial authority would be held by Imperial vicars until Andreas was 18 years old. According to the Golden Bull, those vicars would be the Elector Palatine Frederick V (oh the irony!
) and the Elector of Saxony John George I. Although Frederick V may have liked the idea on being imperial vicar, I can not see the three spiritual electors electing Andreas knowing that two Protestants would share the imperial regency during his minority. This fact leaves an opening for OTL’s Ferdinand II to be elected emperor in TTL. Upon Mathias’s death, the three spiritual electors and Albert (in his position as regent of Bohemia) could cast their votes for Ferdinand. Albert would not want a non Habsburg emperor and Andreas could contend for the imperial crown in future elections. Not having Ferdinand as ruler of either Bohemia or Hungary would have a lot of repercussions on European history.