If I switch broker's and have been advised my fractional shares in my current brokerage account will be liquidated, do I owe capital gains taxes on the fractional shares?

[MSCO9241]

the broker will report the sales to the IRS.  what we can't answer is whether or not the broker will assign any cost to the frac shares. if they don't you can.  you are required to report the transactions on your return.  also, be careful with the new broker.  many times they do not receive the cost basis of transferred shares and instead use FMV on the date of receipt which is totally wrong for reporting purposes should they be sold. 

[fanfare]

there's no law against having accounts at two brokers.

If you don't want to liquidate your fractional shares, don't close the account.