How much cord blood is needed for a transplant?

The crucial thing is not the volume of the cord blood collection, but the number of stem cells it contains. Transplant doctors develop recommendations based on the Total Nucleated Cell count, or TNC, because it is the easiest measure to reproduce between different labs.  

When treating cancer, the transplant dose should be at least 25 million TNC per kilogram of patient body weight (1 kilogram equals 2.2 pounds).  The average cord blood collection holds 8.6 million TNC per mL.  Thus, the optimal transplant dose requires harvesting:
1.3 mL of cord blood for every pound of patient weight, -or-
2.9 mL of cord blood for every kg of patient weight

References:
Reed, W et al., Blood 2003;101(1):351 doi:10.1182/blood-2002-02-0394
Barker, JN et al., Blood 2005;105:1343-1347 doi:10.1182/blood-2004-07-2717
Eapen, M et al. Lancet 2007;369:1947-54 doi:10.1016/S0140-6736(07)60915-5
Rocha & Gluckman Brit. J. Haematology 2009;147(2):262-274 doi:10.1111/j.1365-2141.2009.07883.x