Had a prob sounding much the same as this a while ago. I had run the car pretty empty at one point and thought it may have been dirt come through and fowled a plug or injector. It was only first start up and went away like you say after a minute or so. I am not sure what cured it but did change fuel stations and it seemed to get better and kinda went away! either that or I just did not take note :fishwack:
I did find at one stage a pipe that had perished coming off the top rear side of the injection/air box system just off the right side of the engine as you look into the bay, it was a thin pipe that had perished where it attaches to the box and had not noticed it as it had dropped down slightly. Apparently it is not a major problem, just a vacuum pipe of some description that can cause splutter on initial start and slightly increased consumption initially. I managed to reattach with another piece of rubber hose cut to measure on the end to fit over the existing pipe and connection stub off the main box. If I recall, you wont miss it as there are 2 of the thin hoses, one under the other. Since then I have not experienced any splutter either, so which of the two remedies I did cured it, I'm not sure - probably the latter :=):
Apologies for the poor description but i'm sure you will notice/know which part of the system I'm trying to describe :rollsmile:
(2002 e46 300i)