After emailing, live chatting, and phone calling - the range of answers from Costco to some very high priced labs resulted in this range of results:
There are a bunch of labs who will tell you to send them any file format, any color space, etc. They infer that they are fully color managed. When it got down to it, the "front end" of their process converts everything they receive into sRGB jpegs for printing.
One lab proudly offers a single ICC profile for use with any of their paper selections.
Some want the file with the provided ICC profile used for soft proofing.
Other labs clearly tell you to soft proof to the ICC profile but to send them the soft proofed file in ProPhoto or Adobe RGB.
What I ended up telling the class is to do their homework with any lab, not to believe what the web site says, and that like John Arbuckle, "You get what you pay for."
Interestingly enough, Costco provides ICC profiles for each of their paper/printer combinations, and it is "by store location" specific and they are updated as needed.
Yes, there are different ways how the labs actually proceed regarding color management. Even, one and same lab may offer different ordering and processing paths.
Let's assume that the lab offers an ICC profile for download, from what I can tell there are two basic cases: either the lab operates the printer in a so-called "sRGB-mode", or they make use of the printer's full gamut.
This can be tested by providing a file with rich colors in ProPhoto RGB, and a variant thereof converted to sRGB, provided that both images are noticeable different on screen when arranging them next to each other, softproofed to the printer profile. Then, if the print from ProPhoto RGB is equal or worse than with sRGB, forget it, look for a different lab.
That way I checked out a bunch of labs in my region, found the right one, and against my concerns I'm quite happy with the "softpoof but do not convert approach".
Peter
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