What is the maximum memory size that the motherboard in personal computer in current market can support?
On older motherboards (before about 2006) this was determined by your memory controller, which was part of the North Bridge (also commonly incorrectly known as "the chipset").
Newer motherboards will have the north bridge integrated into the CPU.
Most modern (6th generation intel - Dec 2015) consumer processors can address a maximum of 64GB of memory. This isn't a hardware limitation as it once was. (64-bit is not related to 64GB memory cap either, don't let it confuse you).
The server processors intel markets can address more than 1TB of memory.