Mac Pro - broken piece off of Logic board

can you post a picture?

Once you have an image on your Mac, the little camera icon on the forum will allow you to place that picture in a posting.

And which model-year was this?

Those "little can" capacitors are called electrolytic capacitors, because the little can is filled with electrolyte (an ion-rich fluid) that makes it all work. They are more expensive than solid capacitors, so they are only used where needed and generally cover a group of components, not just one little part nearby.

Many electrolytic capacitors are in strategic places where they help stabilize power supplies. Those near the PCIe slots would be expected to stabilize power supplied to the PCIe slots. A different one would be needed for each Voltage supplied. I know PCIe slots use 5 Volts, 3-ish Volts, and possibly a lower one like 1.2 Volts. 28 Volts and 12 Volts may also be needed.

The general rule is that a larger physical size, a higher Voltage, and a Higher heat range can almost always be substituted with impunity. Leads should be kept as short as practical, and polarity must be followed or the part may fail prematurely.

Did ever find a fix for your board?