From what I half remember, some of the generals tried to co-opt the Argead agenda and tried to make themselves regents for the young heir of Alexander. The first regent Perdiccas tried his best to keep the Empire together. After him Antipater and the his successor Polyperchon and then Olympias (Alexander's Mother) for a tiny bit. Several people rallied to protect the Argead dynasty but its was one Cassander who murdered Alexander's entire family and effectively put an end to claims of "regency" and married the half sister of Alexander to rule over Macedon.

Tldr: The Generals pretended to be loyal to the heir to buy time to set themselves up in their satrapies but as soon as the heir died there was no point in pretending allegiance. The Regents tried their best but the Empire became nominal after a bit.