It also widely depends on the jurisdiction of the account. With HSBC, and to a lesser extent now Citibank (given they round of exits from retails markets in Asia), you can theoretically open account abroad remotely (either online, over the phone or visiting the international banking centres). However, for example, Taiwan does not let you open accounts remotely, so you have to visit a branch if you are a foreigner and show your ARC. You can usually see the list of countries where you can open the account remotely with these banks on their websites in the international banking section.